Hope it helps! This forum helped me set this up, happy to know I might be doing the same for someone else.
For backlight I use the Skier Lightbox, it’s an led panel lit system made for precisely this. Look it up, totally worth the investment to me.
Using a phone or iPad will work decently, but you will need some type of diffusion. Any kind of neutral colored frosted glass or acetate without texture, and you will need the film separated from the diffusion. Otherwise you will probably end up seeing the pixels of the Phones screen in your capture.
Best to get the Skier, or an LED light pad with good CRI and a film holder or tape your film to the surface of anti-newton ring glass.
There are lots of more helpful and detailed explanations than mine about light sources on this forum.
For flat field correction I first load a frame and focus on the grain, then remove the film and take a shot of the blank diffused light source. Because In my case the film is about 1/4 inch from the diffusion, when there is no film loaded I have an out of focus shot, which I capture, and there I have my calibration frame. Then I go about capturing the rest of the roll. This way you should be getting the closest to exact amount of distortion/vignetting since those issues are effected by what distance the lens is focused to.
Chances are, I think, that your light source is causing a lot of these problems.
Hope that helps!