Test Result:
dinput Arcade Joystick (Select Button, 1Joy9)
dinput RetroFlag Controller (Select Button, 1Joy7)
MAME (stand-alone): Works!*
* Standard settings.
MAME (RA): Works!*
* Had to change in MAME "Coin 1 - 5 or Joy 1 SELECT" to "Coin 1 - 5".
xinput Microsoft Xbox 360 Wireless Controller (Back Button, 1Joy7)
xinput RetroFlag Controller (Back Button, 1Joy7)
MAME (stand-alone): Doesn't Work*
* Even changing in MAME "Coin 1 - 5 or Joy 1 Back" to "Coin 1 - 5".
MAME (RA): Doesn't Work*
* Even changing in MAME "Coin 1 - 5 or Joy 1 SELECT" to "Coin 1 - 5".
Something related to dinput and xinput?