So..... I checked the md5sum of the downloaded file and everything is correct. I created a USB stick via dd again and still, I am not able to get it running. dd ran without an error and if/of sizes are correct.
When I start up, I arrive at the blueish welcome screen. Whatever I choose, it will result either in some error message or black screen.
I also tried to boot up with a DVD (max 4x speed), but it is still the same. So, I doubt that it has something to do with the stick or DVD.
I could imagine that the configuration of my PC is not compatible:
AS Rock Motherboard 939A8X-M
AMD Athlon64 3000+ CPU
3GB Ram
200GB Harddisk SATA
Actually nothing exotic. But somehow ot good enough for KaOS, I guess.
If anyone of you has still an idea how to solve it, I would appreciate the effort. If not, I have to wait and continue with Ubuntu until hardware changes.