As cool as that would be, it would take a bunch of work, unfortunately. The different fly poses are just emotes (/em flypose1, for example) that get held while you're moving in flight and drop as soon as your animation would change (basically, as soon as you're not moving forward). To make the current fly boards work with combat animations, they'd need to redo all the animations for every attack just for that use case, and I'm not sure the reward is really worth the effort.
Not that we can't dare to dream that they'll have the resources and time to make little improvements like this at some point, so don't give up hope!
