Birds are more maneuverable than one would expect. I have a bird feeder hanging off my kitchen/diningroom window, and when there is a line to get into that thing, the birds will outright hover for a couple seconds before deciding to fly vertically to land on the roof of the feeder. (And no, they're not hummingbirds.) When birds splat into the window entirely, they're capable of recovering quickly and outright flying backwards before spinning in midair to reorient themselves before flying forwards or nearly directly upwards to pick a place to land.
The primary limiter on flight in birds is not maneuverability, but strength and stamina. Hovering consumes far more calories than gliding or wing beating to move mostly forwards.
I remember seeing several works that show how small songbirds (like a robin) have pectoral muscles that, on a human-sized frame, would be like having pecs out 5 to 7 feet from your sternum, completely blowing any body builder away. They flap infrequently because their body can't store but so much energy, and their dense muscles are prone to overheating if used for so long, so they flap relatively short wings with tremendous strength and speed to gain some positive altitude, then rest their wings and descend in a pattern that creates a sine-curve-like flight path.
Medium-sized birds (like pigeons, or yes, hummingbirds) flap at a continuous pace.
Large birds, meanwhile, have small muscles proportional to other birds (but still larger than the most musclebound human bodybuilder) and, like a weight lifter pressing the absolute limits of their ability in a bench press, can only flap a few dozen times before they wear their muscles down and need to rest. Hence, they prefer to glide over updrafts to save strength between periods where they need to beat their wings.
That isn't to say that a bird can't fly more-or-less vertically, at least for a short time, but that it taxes its strength to a degree that it prefers not to. (Keep in mind, even those slow, cumbersome hawks or falcons are capable of flying upside down for a period to wrestle with other birds while mid-air, and crows being chased by other nesting birds will break from flying position to start snipping at the chasing bird with its beak before going back to flapping its wings to stay aloft.)
Beyond that, many fliers in this game larger than mundane birds are explicitly magical. A flying quadruped FB with no wings just spits (syndrome-laden spit) on your laws of physics.
But more to the point, any coding in the flight pathing is more due to the unfinished nature of the game and its very, very overtaxed, suboptimal pathfinding system for fliers or swimmers. (And now climbers, as well, as evidenced by the significant drop in FPS whenever a climber starts trying to climb to targets.)
DF largely seems to handle non-ground-based pathing via floodfill, which is generally treated as less of a problem by simply making birds fly to points relatively close to their current location, and generally picking destinations at random. Flying creatures that are deliberately pathing to a position inside your fortress (like flying FBs or clowns) are a significantly greater tax upon your FPS. This is also why domesticated flight-capable birds just plain stop flying when tamed and can start adding up to larger fortress populations.
What you need to do is solve pathfinding (and good luck, pathfinding has been a major topic for as long as the forums have existed) and the rest of this is probably already something Toady has already considered.