I'm not clear on whether this would be allowed or violate the self-contained 20 second rule. Each game would start and finish in 20 seconds, but stuff that appears during the game loop can be unlocked by previous games, ie ("player does 5 flicks in a row, unlocks Super Flick each time they do that combo in future games" or new flick proof enemy added to spawn pool). 

This is what we would call progression (like in a roguelite) and that's a little against the spirit of the jam (see the FAQ). If you head over to the discord we might be able to help you brainstorm.