No, keyboard flying not possible.
Youll either have to by a cheap stick (theres quite usable ones for around $15 to $20 USD) or give the mouse a go. Mouse flying *is* way harder to learn, but quite possible.
Come by the training arena (select it on startup screen), you have a two week online free trial period. Theres trainers and lots of other players around, that can help you get airborne. AH is not easy to learn, but very much fun!
You could also get in contact with the training corps via email to
trainers@hitechcreations.com . Theyll be happy to make an appointment with you.