If you go on the torishop, then under misc textures, it says you can buy a flame for 10,000 tc. http://forum.toribash.com/tori_shop.php?cid=55

Is this something you have to have to forge a flame, or is it an actual flame?

No, you need to get another item called Flame Particle.

But can you then use the flame?

Yes, but you need to make the flame first.

10,000 texture for your flame, you need to forge a flame or get someone else to do it for you

The flame in the shop is to texture the flame particle, the flame particle itself is what you buy or forge.
Question answered, therefore, closed.