I’ve been dating this guy casually for a year or so, and he has a partner that he’s been with for almost 10 years. They’re a wonderful couple and we speak openly about our relationships together, but when she’s around he doesn’t flirt with me at all. I know I’m not the main girl, but it sucks being treated differently just in front of her. Do I ask for more attention or should I just look for attention else where? How do I not offend anyone and address this in a formal manner?
Healthy polyamory, and healthy relationships of all types, are about communication! This is totally something that's valid to bring up. Be specific and focus on what's observable. "Hey, whenever we're around Esmeretta, you never call me 'babe'/kiss me/hold my hand/etc. and that's starting to bother me. Is that something specific you two have negotiated, or is this something we can talk about and work on?"
It's possible that he's doing it subconsciously or just assuming that it would be more comfortable for everyone if he acted in this way. A little more intentionality and awareness is never a bad thing!
Don't just assume that because you've been dating him for less time that you're "not the main girl." Polyamorous relationships don't need to be ranked - you can both be on a 'level' where you have his flirty and affectionate attention. Don't relegate yourself to a place where you don't get to ask for what you want because you think that's how things are set up.
If he comes right out and tells you that it's intentional - that he, or she, or both of them are uncomfortable with him being flirty while she's around - then you have to decide whether you want to be in an arrangement where, after dating someone for a year, you still don't get the type of attention you want because of another person's preferences.