No, there is no rules mechanic for this
The mechanic we have for impact damage from high speed is falling damage, with 1d6 per 10 feet fallen, to a maximum 20d6. Falling damage is defined by height, not by speed. Xanathar's Guide to Everything clarifies that
The rule for falling assumes that a creature immediately drops the entire distance when it falls.
How fast you fall is not explicit in the basic rules, and according to the clarification the speed is infinite ("immediately ... the entire distance"). Xanathar then offers an optional rule that
When you fall from a great height, you instantly descend up to 500 feet. If you're still falling on your next turn, you descend up to 500 feet at the end of that turn.
So falling speed is still infinite, as the falls happen "instantly" or "at the end of the turn", taking no time.
OK, but what if we assume a falling speed to compare against?
Of course, infinite speed makes no sense. What if we interpreted the optional rule as a falling speed of 500 feet per turn, which we know to then deal d6 damage per 10 feet on impact?
Normal fly speed is also only 60 feet per second, and if you drag along a grappeled creature, speed is halved, so even after a Dash action to double it again, you would still be at 60 feet per round. This is the falling speed of Feather Fall which we know to not deal any damage on impact. So still no damage.
Wait, what if we were really fast?
What about a rogue that has all of fly, longstrider and haste cast on them in order? Fly gives them a 60 feet speed. Longstrider increases it to 70 feet. Haste doubles their speed to 140 feet. They gain one extra Action from haste, and a Dash bonus action from being a rogue, for a total movement with their normal Dash action and Move action of 4 x 140 feet = 560 feet. That would be even faster than falling speed. However, dragging the creature along will half their speed to 280 feet.
In that case, since the kinetic energy that would be causing the damage on impact grows with the square of the speed, about half the speed would translate to about quarter the potential damage. With an expected 3.5 points per die, this would leave maybe one point of damage per die.
So, unless the opponent has the ability to fly themselves, you would be much better off to drag them up, then let them drop for falling damage. Especially because there are also no clear rules for adjucating how slamming the other creature into the ground would buffer the damage of your own impact.
PS. A word on real world falling speed
As explained in other posts, under planet earth gravity and air resistance conditions, a human falling accelerates quadratically to fall 576 feet in the first round, and up to a terminal velocity of 1,043 feet after the second round. D&D for ease of play does not simulate the physics of acceleration during falling.