It should burn in the same that your fingernail cuttings burn.
I have not yet requested this at the auctionhouse yet, but I assume they will have a problem with me setting their unsold item on fire
Personally I am not very fond of rhino, indeed because it is not always easy to recognize. But also I am more inpressed by craftmenship of the carver, wheter it is in rhino, buffalo, ivory or wood.
The pieces I have seen where complete horns decorated by the chinese, and on those pieces you can indeed easily see the grain/hair structure.