Hi Achim
I have built a flatfield box myself and used electroluminescent foil rather than LEDs underneath a cover of opaque polycarbonate to even out irregularities of the foil. Foil and Polycarbonate are sandwiched between two wood plates, one of which has a dewshield-sized hole for my refractor. Otherwise you only need an inverter and a cigarette lighter plug. I got the electronic stuff here:
https://www.reichelt.de/leuchtfolie-cyan-210x149-mm-el-folie-a5-cy-p60200.html?&trstct=pol_12and the Polycarbonate (PLEXIGLAS® GS weiss WH73 GT 3mm) and front wooden plate (Multiplexplatte Zuschnitt 12mm) with a correctly sized hole here:
https://www.plattenzuschnitt24.de/Plexiglas-GS-weiss-WH73-GT-3mm.htmlDon't forget to line the inside of the wood with velours foil, otherwise you'll get brighter fringes due to reflection off the wood surface. By my guesstimate, all materials will set you back about 70 €, plus you get the fun of assembling the Box (If you like doing that kind of stuff, that is

). It really works a treat, i got rid of the funky pattern background noise and gradients I got using a white t-shirt for flats, and also of dust blobs (I will post a picture where I applied my flatfield box soon). Also I do't need to rotate it as illumination is very even. On the other hand, for 90 € you can get an aurora flatfield panel (160mm) from Gerd Neumann which also uses electroluminescence and might work even better. Mine was cheaper (about 30€) because I only use a small refractor and the foil is the most expensive part.
As for the exposure time of the flats: you want to get as high as possible without leaving your sensor's linear response, before the brightest pixels hit the anti-blooming gate. For DSLR users like me that means the Flat's Histogram peak schould be roughly in the middle of the scale to be on the safe side. For example, on my 73mm f/6 refractor the exposure time is 1/20 s, but that will vary depending on your setup.
Clear skies, Marc