Well, crud. I have no idea why it'd flicker like that. :/
If Alt+F10 (Ubuntu's full screen mode) didn't work any better, we're running low on options, but there is one more thing we can try.
Some Linux-specific issues have been resolved in the past by running Demon using one the following command line options:
-force-glcore32
-force-opengl
-force-glcore45
Which one helps (if any do) will likely be system specific, so I'd just try all three in sequence and see if any resolve the flickering issue in F11's full screen mode.
Sorry for the long wait, but the only solution I could find after moving to Linux Mint was to just autohide my toolbar and play windowed. I definitely feel you should still add some resolution options at some point for the sake of accessibility. Looking forward to finally trying this! I'm a big Megaten fan so this should definitely scratch the itch (no pun intended).
No worries on the delay, I'm just glad you were able to find at least a partial fix.
Regrettably, most of Demon's core systems (including those related to rendering and resolution) were made by me back when I was much newer at engineering (over a decade ago now!): while it would not be impossible to refactor them to something capable of better resolution support, it would be a pretty significant undertaking that I admit is unlikely at this point given Demon is no longer in active development.
I apologize for this and I hope you are able to enjoy the game in spite of the resolution limitations. I am also a big Megaten fan, which is what inspired me to make this game in the first place. :D Cheers, and good luck in the tower!