Yeah, fire can burn on different colors depending on chemicals, isn't that the basis of fireworks too now that I think about it?
So following the advice (thanks once more!), here's what I came up with:
We've got red, green, orange, blue, yellow and white. The big thick arrows mean it deals double damage while being immune in reverse, thin arrows means it deals double damage and receives half damage. There's less relations to remember, and it forms a nice magic hexagram inside an hexagon. The icons should help remember their position in the diagram, clockwise you're always vulnerable to the two previous elements while having an advantage against the next two.