You earn points from the moment you enter Chaos Squad, for killing enemies, accomplishing objectives, racing to the icons that start missions, and virtually everything else you do.
Your goal is to accumulate as high a score as possible in order to get as many spinners as possible, each of which can produce a different reward. Sometimes you’ll just get cash or Overcharge, but you can also get the ProPain Launcher, upgrades to the level-2 versions of many Amps, temporary powered-up versions of your standard weaponry, or new clothes that aren’t available anywhere else in the game.
Your Chaos level is also applied to your final score as a multiplier, which directly affects how many rewards you earn. As you can tell from the score requirements, multipliers count for a lot more in Chaos Squad than your raw score does. You can farm points relatively easily between missions by wandering around the city and killing whatever random enemies you run into, but since the multiplier is what matters, it’s more or less a waste of time.