If you are installing to the same Operating System (OS) - Yes, all mobile App stores allow you to reinstall purchased Apps. HOWEVER - You can't move to another OS without purchasing the App separately for that platform. See why here.
For FL Studio Mobile Android:
Please check the Apple iTunes support web site on this subject:
Downloading past purchases from the iTunes Store, App Store, and iBooks Store
For FL Studio Mobile Windows App:
Image-Line Support Team