My wife wants me to use an FFM 3d printer to make custom stamps for her to use on paper (scrap books, letters, etc.). She is convinced, however, that they will be too rigid to make good stamps. A quick google search showed ones made from PLA and ABS. Logically, though, a TPU or similar would address her concerns. A good quality stamp needs to hold ink and make good, even contact with the paper. It would probably need to be able to be sanded or smoothed in some way.
I am supposed to receive my printer next week or so and am trying to get some filaments, STL files, and accessories I will need ready in advance so I can rapidly learn how to use it.
Recently I've experimented with printing some Nylon 618 filament after reading stuff online about it. I'm using a Craftbot original with the stock hotend, keeping the Nylon dry in a ziploc bag. It prints really well, just tricky to get it to stick to the bed (I'm still working on that), but otherwise it's great.
Once printed, the main difference from PLA prints is the nylon remains more flexible. If you bend a thin nylon print, it tends to just spring back to the shape that came off the printer. That's very different from my PLA prints, which will either stay bent or break apart.
I believe that nylon would be a good material for you to try for stamps, because of this flexibility and shape-preserving quality. The comments show some other materials to try, but I'm limiting my answer here to my own personal experience.