I figured Mercury would be the inspiration. Not many characters with gunboots that I know of.

So let's focus less on the gun boots and more about his combat style then? Obviously his first ability would simply be having gun boots. That's a weapon unique enough that no one is going to be selling it, nor will there be anyone who specializes in it's crafts.

His second ability can be something along the lines of "Longer you move, increase movement speed and stronger your next attack". So basically he builds speed as long as he keeps moving (No standing still) and his next attack increases the longer/further he keeps moving. This way he can literally run in circles around someone and then spin kick their head off.

Third ability will simply be the more he attacks, the faster his attack speed is, though he has to keep the attack up. So it's kinda a switch up between his second and third ability, though he doesn't lose his attack speed from his third ability as long as he keeps moving via his second ability. Thus, he can run and dodge, charge in for burst and stay for a sustained, and then run away if it looks like the enemy is about to CC you.

Though do note for such a hypermobile champ, you probs have the durability of a paper sack. Unless you intend to make a Speed Tank like what Arms Slave will eventually be.