So I’ll answer your questions in parts and as best I can

1: How did Naruto become so big in the fanfic community?

This one is pretty straightforward since Naruto is already one of the more popular Shonen (I probably butchered the spelling there) anime and has lots of room for writing so naturally it took off more then other anime’s (One Piece, MHA, Bleach)

2: How is it so flexible?

The world of Naruto is vast with lots of lore but yet it’s also so empty so this leaves a lot of room for people to come in and write as they please with ease

I mean just think about it you have 4 unexplored main Villages

Hundreds of named and interesting characters with blank backstories

Several world wars with vague events

Plenty of points where the story can diverge realistically

So on and so forth

3: How did it affect popularity?

This one I can’t answer but I can say it’s definitely helped the series stay fresh for many and keep its popularity strong