Both are correct. I'm not sure of the difference, exactly. But I was talking with a dane before, and she explained to me that snakke is more informal. So, you could say "Jeg snakker ikke dansk" and "Jeg taler ikke dansk" but you wouldn't really say "snakker du dansk?". So, in the example of "Jeg taler ikke flydende dansk", you would probably be more formal in the situation where you're needing to tell someone you don't speak a language well. Using snakker instead of taler wouldn't be wrong, but taler would be more appropriate.
Men, Jeg er ikke fra danmark, og jeg taler ikke flydende dansk. I can't answer the question with absolute certainty. If a native danish speaker could chime in that would be awesome.