Hi,
Thanks for your question. No, the Tinkerer will not get a discount. The Tinkerer does not have flying. It has an ability that can give it flying under the right conditions, but that ability (along with most abilities) only works as long as it's on the battlefield. 112.6 and its subrules (which, for brevity's sake, I won't repost them here) goes through the types of abilities that work when a permanent card is not on the battlefield, and the Tinkerer's ability does not fall under any of them.
Likewise, Levitation only affects creatures you control, and “creatures” only exist on the battlefield: on the stack, they're “creature spells” and everywhere else, they're “creature cards”. Levitation won't affect a creature card or a creature spell, only creatures you control on the battlefield, so the Bears would not get a discount.
109.2. If a spell or ability uses a description of an object that includes a card type or subtype, but doesn’t include the word “card,” “spell,” “source,” or “scheme,” it means a permanent of that card type or subtype on the battlefield.
Meanwhile, the Drake has flying. Flying doesn't do much if the card isn't on the battlefield, but it still has flying, so the Warden will give the Wind Drake a discount when you cast it.
In short: the Warden would give you a discount on the Wind Drake. It would not give a discount to the Grizzly Bears if you control a Levitation, and it would not give you a discount on Aeronaut Tinkerer, even if you control an artifact.
Thanks,
Nathan Long
Magic Rules NetRep