OK, that's good.
How big does your list get, how many lines of text?
Internally, Fl_Browser uses a system of linked lists to manage the line entries, so if you have a very long file, with "many" lines, it may become unwieldy in use.
Though, with modern CPU's, I'm not sure what actually constitutes "many lines" these days - I'd assume many thousands of lines, but don't actually know.
In practice, where I have done this, I've tended to hold a few thousand lines in the Fl_browser and beyond that, as more lines are added, pop lines off the top of the browser into a log file (then I can read them back later if I really need to; in practice that doesn't seem to happen as much as I imagined it might!)