OK so all I see on the web is that Kid Quick is easier than Glass Joe and should go down in 0:30-1:00. I do not get this. Maybe I'm an R-tard here but I have never had it easy with this guy.
Alternate method: This guy is actually the easiest person to beat in the game. Throw a right to his head and it will force him to retaliate with a hook. Dodge to the right and then follow with 3 left jabs to the face. Repeat this pattern and he goes down in about 30 seconds. 2 left jabs and a right to the face will force the hook retaliation, speeding up this process if Quick is not as full strength. This is touched on above, but with this method you are forcing him to throw a hook at you vs waiting for him to do it on his own.
In the arcade version of Punch-Out!!, the trick to knocking out Kid Quick is to do the pattern "left, left, right, right" to his head. On the last right, he will throw a low body punch, which requires the player to dodge it and repeat.
These don't ever give me love. When I have beaten him it has been pure luck. I play in MAME, on my Switch and on actual hardware when I go to Funspot. This guy is always a pain in my ass. How does everyone beat him so easily?