Function to return last line's length of a string
It's good that you've used strlen, but there's actually another standard function that could be useful here. Instead of your reverse loop, you can use strrchr to find a pointer to the last occurrence of a character (or NULL if said character is not found). As discussed in the comments, this could be (and likely is) slower in the case when a newline is not found, but unless this function is called very often or is in a very performance critical path, I can't imagine it will be an issue. If you do need to optimize it to your original implementation, I would pull the reverse loop logic out into a function.

Anyway, a bit of a review:


Your string parameter should be a pointer to const since it's not modified.
Personal style thing: I'm not a fan of return (...). If it matters, it also tends to be pretty rare style wise in C.
You should probably explicitly document what happens if a line break is not found in the text. I wouldn't be sure whether strlen(string) or -1 we be returned.