If you do want to increase the protein level in your chickens diet, cat food is not really healthy for your chickens because of the sodium content, which can cause severe kidney problems.
Also, the animal protein in most cat food (dry or wet) is "chicken meat" and that just does not sound right to me either.
Most of the commercial chicken food does not contain animal protein anymore at all. Here are some possibilities to boost the protein level in your chickens diet, but be aware that too much protein in a chickens diet will not only cause nutritional imbalances, it can also cause diseases like Gout etc.
1) You can use "Flockraiser", which is a balanced poultry feed for all kind of poultry and has a protein content (depending on the brand) between 18% to 22%. For laying chickens it does not have enough calcium, but if you always have free choice cracked oyster shell available for them, the lack of calcium will not be a problem with "Flockraiser"
2) Some people use "
Manna Pro" pellets to increase the protein level in their chickens diet, but some chickens are very finicky eaters and it will take them a while (if at all) to get used to it
3) My personal overall favourite protein "increaser" are "Meal Worms": nothing is better than that. Some of my chickens went through a very hard moult last year and were almost naked. This winter I was feeding meal worms every other day and the chickens feathered out so much faster than all the other years, never had bold spots like they did before and always stayed shiny in their plumage. Most of my chickens started laying after the winter break about 3 weeks earlier than last year. Quintessence or meal worms? I am convinced it is the meal worms!