Creatures do have maximum DNA caps per Creature Level based on their rarity. When the cap is reached, any additional DNA acquired in-game will not be added. The only exception for this is for any DNA acquired through purchased incubators.

The maximum amount of Common DNA that can be acquired per Creature Level is 250,000 DNA

The maximum amount of Rare DNA that can be acquired per Creature Level is 100,000 DNA

The maximum amount of Epic DNA that can be acquired per Creature Level is 25,000 DNA

The maximum amount of Legendary DNA that can be acquired per Creature Level is 10,000 DNA

The maximum amount of Unique DNA that can be acquired per Creature Level is 4000 DNA