Fastest character?

Quote from Deltadragonborn >>

What's the fastest someone can go while flying though?

The speed I posted of 5,660 feet per turn can be Walking, Flying, or Swimming due to Stride of the Elements (Monk, Warrior of the Elements level 11 feature) while the elemental attunement is active. I think all of the modifiers apply to flying and swimming movement.

Quote from Deltadragonborn >>

Also, if you pick up a rock, do all this running, and at the last possible moment of the round you threw it at the BBEG, how much damage would that do, and would it keep the momentum?

After running 5,660 feet before the throw, a rock would deal 1d4 bludgeoning + your strength modifier. You might be able to make the case for slashing or piercing depending on the shape and type of rock. You would not add your proficiency bonus to the attack roll unless you have proficiency through Tavern Brawler or a similar feature.

More on topic, you can run full tilt at 5,660 feet through a hallway with 90 degree or greater turns without any concern for safety from the walls. Inertia and momentum don't exist in D&D per se. Terminal velocity is modelled with a maximum falling damage, however, there is no restriction on how far you can fall. Whether you fall 200 feet or 20,000 feet, you take 20d6 bludgeoning damage but still fall the full distance. If you fall from orbit into a swimming pool, you can a DC 15 Athletics or Acrobatics check to take half damage. It's just a simplified approximation. There are no approximations to model inertia or momentum.

the funny thing is that my friends are all math nerds, so they would love that