You probably hit it right on the haed, and will have to remap (actually unmap) the flightstick from mame's digital2analog "ports" to fix it.
Mame has three "input ports" for each analog axis: "XYZ Analog", "XYZ Analog Dec", and "XYZ Analog Enc". The first one is for true analog inputs, the second two are mame's digital2analog ports, so people with digital only inputs can play too. The problem is directInput cannot tell mame if an axis is analog or digital, so mame has to treat anything mapped in these ports as if they were digital. And inputs from Dec & Inc ports override inputs from the plain analog port.
Start a game, press tab, select "Input (general)", select player 1, and go and remap all the "... Dec" and "... Inc" ports so they don't include your flightstick. (And make sure the plain analog does include it.)