No. Image-Line makes FL Studio for Windows and macOS only, and there is no Linux version. REAPER, Bitwig Studio and the free LMMS are the music programs that do have proper Linux releases.
FL Studio by Image-Line · Music & audio · No way to run it
Image-Line is clear about this. FL Studio runs on Windows 10 or 11 and on macOS, including Apple Silicon Macs.
Linux is not on the list and there is no browser version.
Music production is the weakest area on Linux for a Windows switcher, and it is worth being blunt about why. It is
not the program itself. It is the plugins. The instruments and effects you have bought over the years are Windows
files, and most of them will not load on Linux. That collection is usually worth more than the program, and it is
the thing that keeps people on Windows.
The second problem is that project files do not travel. An .flp file opens in FL Studio and nothing else. No Linux
program will import your arrangement, your automation or your mixer settings. Moving to a different music program
means rebuilding your songs, on Linux or on Windows, which is why many people keep one Windows machine for music
and move everything else across.
If you are willing to start fresh, the Linux options are genuinely good. REAPER and Bitwig Studio are paid programs
with official Linux versions from their own makers. LMMS is free and is laid out along similar lines to FL Studio.
Before you wipe anything, export every project as audio stems, one file per track, so you keep your work in a form
anything can open.
Free, and its piano roll and pattern-based way of building a song are the closest thing to FL Studio's. Weaker at recording live instruments and less stable with plugins.
Your files: Cannot open .flp files. Import your exported audio stems instead.
Paid after a 60-day free trial, with an official Linux version from Cockos. Excellent at recording and mixing, but it comes with almost no instruments.
Your files: Cannot open .flp files. Works from exported audio stems.
This doesn't have to stop you
One stubborn program doesn't have to decide the whole question. You can keep Windows on the same PC and restart into it only when you need FL Studio. Everything else you do can move.