Sorry it's not working for you. Unfortunately, I don't know what could be causing the problem. I'm able to launch the game just fine on my Intel Macbook Pro with Monterey 12.7.2. Do you get any error message? You could also try checking if there are any errors in the flare_log.txt file found in ~/.config/flare/
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The icon shows in dock for a fraction of a second, and then disappears. The app never starts, never opens a window, doesn't give an error message. Nothing gets written to flare_log.txt, its created, modified and last opened dates are from yesterday (when I reinstalled 1.14 to see if that still worked.) The only error in it is "ERROR: FileParser: Could not open text file: engine/number_format.txt: No such file or directory!"
I noticed on the website it says the Mac version is for Intel 64 bit. Maybe it isn't supposed to work on Silicon Macs?