This section is more for xbox 360 hardware and accessories for use on the 360 but can still answer things if it is for Windows or similar usage. If it is for the 360 then I don't think there are any meaningful ports of flash or one of the flash recreations.
For Windows/Linux/whatever I doubt many flash games will be programmed either to speak to the pad or speak to OS level controller stuff.
That said many things are not programmed to either speak to the pad or speak to the OS level controller stuff so we do see tools to help out here by turning joypad presses into keystrokes and mouse movement. For many years the tool of choice was called joy2key but there are others these days
https://alternativeto.net/software/joy2key/