I conquer battlefield with purple Kennen on oponnent's turn with Ride the Wind. I give flow to action speed spell. Can i use it with flow in my oponennts turn?

Yes — but only if the spell can legally be played at that moment, because Flow grants no timing permission at all (Rule 829.1.b.2: playing for Flow cost doesn't change when the spell can be played, only which zone it comes from).

So the spell's own keyword decides. If it's an [Action] spell, it's playable during a Showdown on any player's turn (Rule 806.1.b), so on your opponent's turn you can play it from trash for its Flow cost during a Showdown Open State with focus and an empty chain — that's the only window an Action spell ever has on someone else's turn. If it's a [Reaction] spell, same thing but also during Closed States. If it has neither keyword, you can't play it on your opponent's turn at all, Kennen's Flow grant notwithstanding.

One timing trap: Kennen's "When I conquer" trigger fires as the showdown closes/control is established, so there's no showdown window left at that instant — the turn goes back to the opponent's Open State, where the turn player gets priority and you can't play an Action spell. You need a later showdown that same turn (e.g. the opponent moving a unit into a battlefield); the granted Flow only lasts that turn.