Here is a way:
Drop this screen called: "1024jogcontrol.set" into your main mach3 directory.
Goto Config>system hotkeys>in the OEM trigger1 box put the number 12 hit ok
Goto Config>Ports and Pins>Inputs tab scroll down and enable OEMTrigger1 set the port and pin you want to have OEMTrigger1 come in on. Hit Apply, ok. (make sure you got the active high or low correct (or auto set), depending on your system.
when you push your external button that comes in on OEMTrigger1, it will pull up the "Jog Screen". NOTE: I tried to have screen 50 activate but it doesnt load correctly, since I have no way to "Push" the Tab key itself and emulation doesnt work correctly. so I just moved the Jog control to screen 12.
Flash can actually "Push Buttons" or emulate Button Push calls, so you could probably do this in Flash exactly like you want, but this is the only way I personally know how to bring it up.
Scott