There are two specific gene pairs that form the base for a comb type. The pea gene and the rose gene. If a chicken has only the pea gene then it has a pea comb. If it has the rose gene (like yours) then it has a rose comb. If the chicken has both pea and rose genetics then you get a walnut comb. If a chicken has neither the pea nor rose genes then you get a single combed chicken.
But the fun doesn't end there. There are other genetics that affect the appearance of the comb, whether rose, pea, walnut, or single. A comb may be small or big. It may stand upright or flop over some. There is one that can make them a Vee shape like the Polish breed, another gene that can make them more of a cup shape like the Sicilian Buttercup breed. Lots of variation.
What I think you are seeing is a rose comb with additional genetics that make that one look kind of flat.
Chicks generally undergo two or three juvenile molts before they reach full size. They outgrow their feathers and need to replace them. At 12 weeks I would not be surprised that yours is molting. Some are fast molters and drop a lot of feathers at a time. These can look pretty ragged while slow molters look pretty smooth even when molting. Have you seen some feathers that color floating around?