How much of the dragon-hoard was claimed by Bard?
We are given this information in the last chapter of the book, after the end of the war and the death of Thorin. In spite of how the situation changed, we are told that the original agreement made between Bard and Thorin stands:
Yet a fourteenth share of all the silver and gold, wrought and unwrought, was given up to Bard; for Dain said: "We will honour the agreement of the dead, and he has now the Arkenstone in his keeping."
Notice how this stresses the honourale nature of Bard - he, although very clearly having the upper-hand after the battle, still gives the Arkenstone to be buried with Thorin, and the dwarves, now having shaken the gold-fever from themselves, recognise the right of Bard to receive a fourteenth of the treasure.