I have the same problem. Since i update to ios 13 or 13.1 or 13.1.1 the issue is still persisting. I recommend everyone to do a downgrade to ios 12.4.1. When you do that, the black camera issue is fix. So the problem is a software problem of ios13. Here you have the link to download ios 12.4.1: https://ipsw.me.
The steps to do the downgrade are the following:
1)Connect the iPhone to the pc.
2)Open iTunes
3)Press left-shift botton and the "Restore iPhone"
4)Select the ios12.4.1 file you have had downloaded
5)Wait until the process finish and ... UALA!!
I hope the future´s ios 13 releases fix the problem.