I used to record in a separate application, until I realised how crazy the workflow was compared to it just going direct into the main project.
FL has comp lanes for recording doesn't it? As in, you can record in a loop over and over and it just keeps creating takes on a new track each time? (I don't use FL so pardon my ignorance). That'd be a much more seamless way of doing things, provided your computer can playback everything and record at the same time that is. Way better and quicker than mucking around with 3 programs IMO. Do takes into project, align them, punch in record an overdub to fix that particular word you didn't hit right, align, make sexy, repeat.