I don't know about FL, but in Ableton you can warp an audio clip to hit right on the beat. When I first started recording guitar, I was having some major latency problems, and being able to warp it back into time was a godsend.
Building your skill of keeping the beat will pay big dividends...but definitely, don't erase all the human touch. Robots are overrated.
Also...sometimes, I like to purposefully swing things and creatively go off the beat a hair (especially with guitar solos) and I've found that even in those situations, the most important beat to stay in time with tends to be the first beat of each bar. So, depending on what you're trying to accomplish, you might get what you need and save a lot of work by just concentrating on getting your audio to hit on the first beat.