hi friends, when someone gifts you a flower, is the flower supposed to go to your inventory? if not where can you pick up the flowers that people have left for you?

No, you don't actually get the flowers left at your profile. You get coins in exchange for them instead (:

oh okay great, thank you!

Because this is confusing, I'm going to add to what Darkrai said. To "give someone a Vesnali flower" you need to go to their User Profile and click on their Option Box (it has a flower in it, for Vesnali). In game terms, this uses up the flower and results in Vesnali Coins. It's never been said, but presumably in imagination you've got a ton of vases in your (non-existent, since there's no such game-thing in Subeta) home, and nobody would be so crass as to re-gift a Vesnali flower, so you can't use the vased flowers again.

This is not the same as giving someuser the flower itself (they're pretty, and people collect them) or any other item, which can be done via the Give to Buddy option or can be wrapped for gifts in Arctic Frost This results in them getting a flower(or whatever other item) but doesnt get you any coins.