Fish sauce is not always gluten-free. I treat it with almost the same caution as soy sauce.
Based on my own research, here are a few gluten-free brands. Most of them are authentic Asian sauces.
Red Boat
Rufina
Three Ladies
Three Shrimp
Squid
Thai Kitchen
-Succulent Succotash
I am Korean American, but have not made Kimchi myself. Most traditional Korean kimchi's include fish sauce. I recently realized this when my mother-in-law told me as I was about to try her daikon kimchi. After research, it is apparent that many kimchi recipes call for fish sauce (Korean aekjeot).
Depending on the brand of fish sauce, it may NOT be gluten...