It's welcome. But I think that her attempting to flirt with way more than one or two person isn't really a good look, like at all. If it was a man thirsting after the ladies while going "ew men smelly xD" I'm doubtful it would've been very well received, because it's kind of creepy and shameless.
People should stop complaining about this kind of things. If she is lesbian, that's fine, if she is not is fine too.
Complaining about sexuality or supposed sexuality is intolerant. For both sides.
Please, listen to the interactions again. Most of them refer to her liking looking like other female champions. If anything, that implies she has an issue with her selfimage. Especially with lines like "I wish I could stay like this forever". The only flirty one is the one for Shyv - and it's a goddamn lunch invitation. I doubt anyone would care if a man invited some lady to a lunch in one of his interactions. There are a few lines that could be interpret to her having an interest in Nami... Which is also understandable since Nami is a Vastaya. And that one line with Evelynn, that can mean MANY different things, considering that Neeko takes on not only the physical appearance, but also a part of the champion's mind when transforming. Also, contrary to what you claim there are both male and female characters that flirt with more than one other champion.
EDIT: also lines about Nidalee... Her past love interest and a friend. And those lines are just general statemets of admiration (like the interaction with Rengar) or just saying she misses her.
