Yes, sort of (with the optional rule for falling onto creatures)
Tasha's Cauldron of Everything includes an optional rule for falling onto another creature. I won't quote it in full here, since TCE is not a freely available source, but the basic idea is that the creature gets a chance to dodge you, and if it fails, the fall damage is split between it and you. The standard rules for falling say that the maximum falling damage is 20d6 (representing an impact at terminal velocity), which results from falling from at least 200 feet. So, if your suggested maneuver is successful, you and the BBEG would each take approximately 10d6 damage (technically you should roll 20d6 and divide by 2, but close enough). So, if you are willing to take that much damage yourself in order to damage the BBEG, then this plan may well be worth it. But keep in mind that the BBEG still has a chance to dodge your human(oid) missile, in which case the full 20d6 damage goes to you.
One potentially important technicality is that in terms of the mechanics, you can't exactly "pull out of a dive" and preserve your falling velocity to hit the BBEG flying horizontally, because D&D doesn't actually have mechanics for momentum. If you use your fly speed to start moving under your own power, this stops your free fall. There's simply no way to represent the concept of preserving momentum within the very simple movement mechanics of the game. However, as long as there is empty air above the BBEG, you can just use your fly speed to position yourself directly over them and then stop flying (assuming you can do so by e.g. folding up your wings) in order to fall straight down onto them. Even though this involves flying horizontally first and then falling vertically second, if your DM is generous, they might allow you to describe this process as a diving tackle, and they might even allow your momentum to knock the BBEG sideways, perhaps with a strength save to resist or something (which wouldn't happen if you were just falling straight down).
I bring up the idea of the DM allowing this because it is entirely within the intent of the rules for DM to do so if they so choose, even if the rules themselves don't specifically allow for it. As the famous passage from the introduction to the DMG says:
As a referee, the DM acts as a mediator between the rules and the players. A player tells the DM what he or she wants to do, and the DM determines whether it is successful or not, in some cases asking the player to make a die roll to determine success. [...]
The rules don’t account for every possible situation that might arise during a typical D&D session. For example, a player might want his or her character to hurl a brazier full of hot coals into a monster’s face. How you determine the outcome of this action is up to you.
(Note that the "you" in this passage refers to the DM, since this is the DMG.) So I recommend that you ask your DM if they will allow something like this, in addition to asking them whether you will be using the optional rule cited above.
Note: If you expect skydiving to be a regular part of your group's adventuring, your group may also want to refer to the Xanathar's Guide to Everything optional rule for rate of falling, which basically says that you fall 500 feet per round (see the source for details). With this rule, it will actually take you 3 rounds to fall from 1500 feet.
