Is it safe to eat frozen flatfish with brown color?
As long as your fish has been handled and stored properly, there shouldn't be any safety issues.

Most all flatfish have a dark side and a light side. (There are only a couple that don't.) Their eyed side would be the dark side and their blind side is the light side. This doesn't just apply to their skin, but to the meat as well. So, if you filet a flatfish, the meat on one side will be white while the meat on the other side will be dark. Typically the dark side will be thicker.

There is a slight difference in the taste and texture between the light and dark meats. What I see served most often in restaurants is the white meat.

All said and done, taste is subjective. Some people prefer the white meat and others prefer the dark. Personally, I find the white meat to be a little more delicate in both flavor and texture. But I like both. I use the white meat for more delicate recipes, e.g poaching, serving with sauces, etc. I tend to use the dark meat when frying or in heartier dishes.

My answer is based on the experience of catching, cleaning, filleting, and cooking flatfish. For anyone interested, PBS has an interesting and informative article about flatfish.