Did'ya think Braeburn was the only pony in the Apple family that made others question their orientation? Oh ho ho... how wrong you were!

This is a simple jokey image I made as a sort of callback to the old "Everypony's Gay for Braeburn" meme, and a sort of way to show how I feel AJ's such good partner material that she's everyone's free pass. This is also NOT my usual headcanon for their sexualities, but I wanted to give'em more... nuanced and varied sexualities, and these are the ones I picked.
It's also pride month and seeing everyone post things about the way they think the characters are and all, I decided to give my own opinion, with a bit of a jokey twist, of course hehe. Obviously, this isn't meant with any kind of malice, and I understand completely that orientation and sexuality are complex and important things and don't work like this. So yeah, I hope you like it!

I'll also provide a little explanation of the flags and all, 'cause there are quite a few in the LGBTQ+ community and they are constantly changing, updating and diversifying so it's understandable if y'all don't recognize'em all. I'll also take the chance to explain why I chose which for each character. Also, a disclaimer... while I tried to do some research on each before doing this, I am by no means an expert on all these different orientations and if anyone has any pointers or anything, respectfully let me know and I'll do my best to update the image and/or the description if necessary.

Glossary
Twilight Sparkle: Asexual - Lesbian
Twilight's first flag is the Asexual flag. This is meant for people who can and desire to form romantic relationships, but have little libido and don't necessarily desire sex with others. This doesn't mean you hate it or never have sex or masturbate or can't have bouts of lust, but there's a large lack of... desire or preference. I think Twilight is the kind of pony who's most caring about the emotional side and the joy of friendship and family and just the warmth of it all. She spent a lot of time away from most and has been thrust into a sort of motherhood with Spike from a very early age that probably really limited her interaction with other ponies her age. She has a super important relationship with Celestia, but it is more... infatuation and respect than having the hots for teacher. I feel she can have and desire emotional relationships, but overall doesn't have any particular interest in getting physical.
And then along came AJ, and well... she's a looker. She's cute and strong and kinda sun-coded... she more than ticks all her boxes in the emotional side with her care for others and for family, her honesty and care, but she also hot enough to get Twi a bit. It also helps her admit she definitely wouldn't say no to Celestia in that sense either, so her second flag is the 5-Striped Sunset Flag.

Fluttershy: Straight Ally - Bisexual
Fluttershy's first flag is the Straight Ally flag. Kinda obvious, but this flag is meant for people who are straight, yet support -often actively- equality in rights and stuff for LGBTQ+ people. Why Straightshy? Well, I think next to Pinkie and Cheese Sandwich, Fluttershy and Discord are the canon-est of the canon ships, and thus is hard to give her anything less. However, while I think she likes and admires a lot of mares in her life, she isn't normally attracted to any.
With... one exception. The one mare she can always fall back on, the strong, capable, supportive and tough farmmare who has helped her a million times over, and has always been happy to go the extra mile for her. And so her second flag is the Bisexual flag.

Pinkie Pie: Pansexual - Polypansexual
Pinkie's first flag is the Pansexual flag. This is meant for people who are attracted, romantically or sexually, to people regardless of gender. Unlike bisexual or polysexual people, who like many genders specifically, pansexuals just don't care for it. Some people may call'em "gender-blind" in the sense that they just don't factor in gender and sexuality in the attraction equation.
I think this fits Pinkie Pie's personality quite a bit, she's a friend to all, mares and stallions, young and old, ponies and non-ponies with little to no care for the differences. She probably can't even understand people who don't see it so simple. Cheese Sandwich is her partner, and she loves him because they click at a deep level, and where he a female dragon wouldn't have changed a thing.
But Applejack is also an amazing pony, sweet and hot like a yummy treat, fun and helpful and an all around good gal. Liking Applejack won't stop her from loving her Cheese Sandwich, but likewise, being in a committed relationship with Cheese Sandwich won't keep her from wanting to add AJ to the fun. Haven'tcha heard about Apple and Cheese Pie? This is why Pinkie's second flag is a mix of the pansexual flag, with the polyamorous flag. A flag meant for people who believe in polyamourous relationships, AKA having multiple partners.

Rainbow Dash: Aromantic - Demiromantic
RD's first flag is the Aromantic flag. This is meant for people who don't want to form deeply romantic relationships. This is basically the other side of the coin in a way, to asexualism. And many times they go together, but not necessarily. In this case, being a sexual aromantic, means that you desire others, have lust and strong sexual attraction and may enjoy it all, but don't care to form any romantic love relationship. They enjoy sexual physicality, but some may not like certain kinds of physicality that are most often connected to romance, like hand holding or cuddling. This doesn't mean they don't feel emotions, or even love for anyone, it's just not romantic in nature. They aren't emotionless robots, they can even be quite emotional and attached to friends, family, pets, etc.
This is the kind of aro I can see Rainbow Dash being. She's loyal and cares deeply for others, she's emotional, but not in a deep romantic sense. She would give her life for her friends and Tank, but she doesn't feel the same kinda heart pang of romantic love. She enjoys physicality, and she likes to express it with competition and rough checks, she enjoys sex, casually or with friends with benefits, she enjoys cuddling her pet and hugging friends, but she doesn't like other more romantic displays of affection, especially publicly.
However, she does feel a much stronger connection to Applejack that does bring her that certain heart flitter and she feels "matched" enough to lower a guard, and allows further private displays of affection. This is why her second flag is the Demiromantic flag. Sometimes considered a subset of aromanticism, demiromantics (similar to demisexuals) rarely ever form strong romantic relationships (sexual desires), and can only do so for very specific people after they've formed a very strong and deep emotional connection. It's not just that they're selective, they just don't form it at all until quite deep into the relationship. It's like... the opposite of love at first glance.

Rarity: Bisexual - Lesbo-leaning Bisexual
Rarity's are probably the easiest and most easily understood flags, but still... Rarity's first flag is the Bisexual flag. This is a flag for people who are attracted to BOTH male and females. Note that I emphasized BOTH. It means they like things about both genders, but they do see those genders, they aren't "gender-blind" like pansexual people. To put a dumb metaphor, bisexuals see the differences in sweet and salty food, and like'em both differently, while pans just like good food and don't see a distinction or reason between the kinds. And unlike polysexuals, bisexual's preferences tends to be within the male-female binary norm (although not necessarily).
I think this fits Rarity because we've seen her gush over many a-guy, but also quite a few ladies as well. She is in a line of work where she sees plenty of good looking guys and girls and has an eye for appreciation, so I have no doubt she appraises them thoroughly. She's also classy and refined, but not backwards and conservative. But for all the grief she gives her, I think she has a soft spot for Applejack and gets riled up easily in her vicinity. And especially seeing her chance is clear after learning about AJ's preference, it's no surprise her flag changed to a slightly modified version, accentuating her preference for the female form.

Applejack: Lesbian
Applejack's only flag is the 5-Striped Sunset Lesbian flag. That's a mouthful, but a bit of a necessary one. Being one of the somewhat oldest/"original" defined and flagged sexualities, it's no surprise the flag they use for recognition has changed quite a lot over time. Some due to being very specific, some due to excluding certain kinds, others due to being tied to questionable actors, the newest and most apropiate flag nowadays tends to be the Sunset flag, either in its "full" 7-striped version, or its simplified 5-striped one. Anyways, doubt anyone needs much of an explanation on lesbians, but it is the flag for women who are attracted to women.
I think Applejack is a mare who likes the female form and can appreciate it greatly. Regardless if it is the smart and nerdy cute kind, the soft and gentle sweet kind, the hyper and bubbly crazy kind, the tough and athletic tomboyish kind, or the prim and proper princess kind... And would you look at that, if she isn't surrounded by exactly those kinda mares...