Smaug is not the last of the fire-breathing dragons. He is the last of the great dragons, perhaps, but Tolkien suggests in one of his letters that other dragons survived into later ages, and Chrysophylax (from FARMER GILES OF HAM) and Beowulf's dragon were two of them.

I quote from Letter 144:

  Some stray answers.  Dragons.  They had not stopped; since they
  were active in far later times, close to our own.  Have I said anything
  to suggest the final ending of dragons?  If so it should be altered.
  The only passage I can think of is Vol. I p.70: 'there is not now any
  dragon left on earth in which the old fire is hot enough.'  But that
  implies, I think, that there are still dragons, if not of full primeval
  stature....