FLStudio cant track and sync audiofiles even if they are rendered from within the FL project itself.
Look at how pro tools, logic and live handles recorded audio with tempo, which makes much more sense. FL goes totally out of sync ...
FLStudio without latency using Asio4All? Of course I am sure there will be some drawbacks if there is a trick for doing so. Basically a way for direct monitoring with Asio4All.
If not, is there a cheap sound card ...