Flaps are not an axis you can map. You've got basically what I've read others did.
Here's what I've read:
Depending on the software you have to turn that axis into a banded slider. It has to have 3 spots, a center which is mapped to nothing, a top which is mapped to "flaps up" and a bottom which is mapped to "flaps down" and basically when you push the lever down it's hitting the Q key repeatedly. You have to shift it back into neutral (middle band) when you have the flap notch you want. Then you have to do the same to retract them: shift it up until you get the notch you want and then slide it back into neutral.
(sounds a lot like what you experience)
That is how others have described their attempts at mapping flaps or trim to certain axis.
IMO, It's FAR FAR easier to just use 2 buttons, one for flaps up, one for flaps down, and I just hit those. I've got a CH throttle quad which has rocker switches, and have one of them as flaps. It rocks up and down so I just mapped that to flaps up and down.