It's possible to generate mates in 1,2,3 etc with tablebase, but that's probably not what you want. You should understand:
- You will need good programming knowledge
- You will need a week generating 6-men tablebase mates
- You will generate too many mates than you can possibly study
If you are confident in programming, you can do this:
- Modify the Gaviota tablebase generator (ask the author for source code). Find where it calculates distance-to-mate, if it's one (or two or three), print the position out.
- Modify the Syzygy tablebase generator. Syzygy reports distance-to-zero, so you may need to use online probing (e.g. Nalimov) or an engine.
- Use the public API in https://syzygy-tables.info. Start from a randomised position. Use the API result to move your position to mate-in-one.
If you don't have any idea what I'm talking about, generating mate positions with tableabse is not for you. You should:
- Buy a book with mate-in-one positions. There is an Android app that can read a chess diagram and convert it to PGN.
EDIT: You shouldn't generate total random FENs. You should try to generate FENs that either side has an extra rook, queen etc.