On Apple Silicon (Mac Studio M1 Max) this worked for me.
1. Install with Homebrew
This will install it as cask, even though it should not be; you can see it under fly -> /opt/homebrew/Caskroom/fly/7.9.1/fly
brew install fly
2. Navigate to symlink in Finder
In my case I ran:
cd /opt/homebrew/bin
open .
3. Find fly link
Then Right-click and hit Open in the warning dialog. Terminal will briefly flash. You should see the synopsis for running fly and "Exited" at the end. Close that terminal window.
4. Verify
Just run:
fly -version
In my case the output was 7.9.1