If a flow card is in trash, and you conquer with Kennen, can I play using kennen’s flow cost instead?

More clear answer, previous could infer you can play the cards only in showdowns or reaction in any player's turn

Yes — you choose. Both the printed Flow cost and Kennen's granted Flow cost become instances of Flow on the same spell, and the controller picks which one to apply when playing it (Rule 829.1.c.3). Worth knowing: Kennen's granted cost is "equal to its cost," which is checked against the spell's printed cost (Rule 206) — so it's usually the base cost, and for most Flow spells (e.g. Shadow Dash at [5][A][A]) Kennen's grant is the cheaper option. You're never forced to use it; if the printed Flow cost is lower, take that one. Two timing notes: the grant only lasts that turn, and Kennen's "When I conquer" trigger resolves as the showdown closes/control is established, so there's no showdown window left at that instant (FAQ #12519) — you need a later legal window that same turn (a Showdown for an Action spell, or any priority if the spell has Reaction if these happen on your opponents turn or during your turn when the turn is in the Neutral Open state, which is when no Chain exists and there is no Showdown active). Either way, playing it from trash banishes it after it resolves.