It should burn in the same that your fingernail cuttings burn. A sort of melting burn unlike charring of wood. I have two African staffs which I believe are Rhino horn. The ends are carved as people and holes have been made for the eyes, set with stone in one and glass beads in the other. These holes have been made by something hot poked into the material, when you look close with magnification you can see the edges are a melted burn like burning fingernails. I hope that helps, the trouble is finding a place to make a test?
Just realised all? horn is keratin. If it is solid and 1m long it not so difficult. Rhinos can grow horn up to 2m. That would look huge as a stick in your hands. Stick it on the bonnet of a small range rover motor car and it will look a lot more modest.
This mention stuff about length if you read carefully.