Always Be Moving
You’ve developed a unique fighting style that uses momentum to keep enemies on their heels. At 3rd level, you do not provoke attacks of opportunity as long as you move in a straight line for your entire movement after the attack of opportunity would be provoked. Additionally if you would move at least 15 ft in a straight line directly before making an unarmed attack or attack with a Brawler Weapon, you can choose to attempt to shove the creature. On a hit the target of the attack must also make a Strength Saving throw versus your Brawl Save DC or be pushed 10 ft in the direction of your movement path.
Momentum Blows
Speed equals force, a concept you know well. At 10th level if you move at least 10 ft in a line before you make an unarmed or brawler weapon attack you deal additional damage on a successful hit. The additional damage starts off as 1d4, but the die size increases for every additional 5 ft of movement before the attack is made, to a maximum of 1d12.
Revved Up
Once you get moving its hard to stop you. At level 14, effects that would reduce your movement speed are halved (rounded up to the nearest 5 ft increment).
Line Drive
You are unstoppable once you get going. At level 18, if you use your entire movement speed to move in a straight line you can choose to attack any number of creatures in the path of your line. If you choose to do so, Momentum Blow’s damage is calculated from your final movement distance instead of the distance before the attack is made.