I have a Thrustmaster T-Flight Hotas X Flight Stick that unfortunately doesn't seem to work on older sim games like Strike Commander. Anyone know if there's a modern joystick out there that DOS era games such as the ones on GOG will read?

Can you not use some mapping software a bit like the xpadder but for joystick, now I don't use a joystick, but a quick google threw up:
http://download.cnet.com/World-of-Joysticks-Emulator-Extreme-Edition/3000-2121_4-76182998.html#rateit

I use a Logitech 3D joystick and it has worked with every retro game I've got through GOG so far. Also works with a few other games that I didn't get through GOG like Silent Thunder A-10 Tank Killer II. It is indeed possible that your joystick may need configured though. If you haven't already checked you may look in the control panel to see if you've got a program for controller or joystick setup.