How does one flirt while polyamorous?

So I'm poly and I have no idea how to flirt. A lot of people say "I want to spend my whole life with just you" and stuff like that, but what for poly people?

First off, I'm assuming you mean "flirt" when already in a relationship? I always associate flirting with trying to get someone's attention and subtly telegraph your interest and gauge theirs when you have a crush on them - once you're secure in their affections for you, it stops being flirting (in my mind). For the record, it's never a good idea to say something like "I want to spend my whole life with just you" as a way to try and probe for someone's interest in you or signal yours without being sure how they feel!

There are many, many ways to express affection for someone without implying a monogamous relationship or worldview! One of my partners often says "I'm on your side," which carries a lot of meaning between us. One of my partners calls me "boo" - pet names can be great flirting tools! Saying things like "you're wonderful," "I really like spending time with you," "you make my life better," "I enjoy you," etc. etc. etc. don't require a lifetime commitment to monogamy! Use whatever compliments fit you and your partners and feel genuine.

Sweet gestures are always great too! If the flirt-ee likes matcha green tea, bring them a little green tea candy that you saw in a Japanese store. If they like sloths, message them a picture of a sloth. If they've been stressing about an errand, offer to run it with or for them. Sharing experiences is a powerful way to show affection: listen to a band or read a book that they like so you can talk about it with them. Inside jokes are great too!

Some people flirt with teasing, but be careful not to get into the territory of "negging." Playful, silly banter and getting into good-natured mischief together is great! Trying to put someone in a position of feeling put down or in danger of losing your respect is not good flirting practice. 

You can also flirt with physical affection - one of my partners and I have an elaborate game where we are always trying to blow raspberries on each other. Butt taps, pokes, smacks, and caresses are frequent between me and my partners. If you're not actually physically involved yet, flirting classics like borrowing their hoodie or touching their arm are classics for a reason. Never underestimate the power of eye contact either.