The creature uses leather gloves that only expose the finger tips(for the claws), these gloves have a insulating "bowl/groove" inside its palm or on its knuckles with desired flammable material inside. The heat will not penetrate the insulation, so the creature shouldn't mind.
How will it work?
You will have some sort of strap holding this device on the hand (this can help you get rid of it quickly if the device fails, so it does not burn your hand) Remeber that the creature has gloves on, so any sparks or hot coals brushing against the hand can not harm it.
Next is the bowl attached to the strap, this could be ceramic, stone or even thick or wet wood. It depends on how long do you expect the device to last. I think the best and cheapest and most primitive way would be some hard wood wiped with clay on the inside.
Next is the flammable material in the bowl, this could be any solid fuel or a medium doused in flammable liquid.
The last part is the most technologically demanding thing (we are talking bronze age or so) You will need wires. They are complicated to make with primitive technology, but they were used both in medieval and ancient eras. And I don't mean like "they could make these", but "They were made for something uselful" Like this.
So once you get some wires you create some sort of mesh and you put it over the bowl with the fuel inside. The mesh will allow the air to flow, feeding the flames, when the creature moves its hands around. You attach this mesh on the sides of the bowl. You can drill holes in the sides for the wires.
And now your "Flame paws" are complete. Now with the strike of your palm (tiger stance) you shall turn thy enemies ablaze. Apply more flammable substance on your target in case it is not flammable enough.
The burning bowls of the Kitty the Scorcher, The searing claws, The doom of the flammable folk!