Even before they could begin to fall, Luke used Flamethrower on the wound. While he had to burn his arm a little as well, he could withstand the pain. His whole arm broke during the last two attacks, so the power added by some flames was nothing… In any case, by cauterizing the wound, Frank wouldn't be able to heal… At least for the time being.
After burning the wound a bit, Luke saw Frank's katana approaching his neck. In the end, he had to let him go and use Checkpoint to escape the attack, but he also used that because he would instantly return to the ground while Frank would have to fall for a couple of seconds.
