Electrically speaking, the Afterburner controls are just two analog joysticks (and one of those only has one axis- the throttle). The Dual Strike/PC flightstick hack, or an
AKI, or an
A-Pac should all do the trick.
I'd lean towards the AKI, just because it can put three axes on one controller. The A-Pac would show the throttle on a separate controller from the joystick, as far as Windows is concerned. This would probably work fine in MAME, but might not work so well if you wanted to use the controls for other PC flightsim games. If you go the hack, you'd want to hack a controller with at least 3 axes on it, and you'd probably have to replace the potentiometers on the Afterburner controls with 100k pots to match the flightstick you're hacking.
Hope this helps!