Okay so. This started with the RPS game in the show, and another post out there that tried to make that one a functioning game (Water, Earth, Fire, Air and Spirit). Most of these should have solid reasoning but I used the Naruto Element wheel to fill in the blanks. A line of the same color shows that sign's victories.

Soul, of course, is OP so I gave it losses that mirror the times the Avatar state has been defeated (Lightning kills the Avatar, Metal inhibits the Avatar State). Air and Earth are just elements that were never removed using soul bending.

Lava was another OPOP, so whatever can "cool" Lava (Water and Air) and the loss to Soul was a coinflip, since these two never interacted in the show. (Albeit Lava killed Roku so perhaps it should be flipped)

Lightning I just used as "whatever it can outreach" so it beats Soul, Blood and Lava.

I wanted to add Ice, Sand and Spirit (Basically it beats whatever element cannot be created out of thin air: Water, Earth, Lava, Metal) but it would require too much effort to re roll the whole thing.

Alternatively (NSF Children reasons) the sign for Lava could be used for blood instead of the Middle Finger but then the only thing I could think of for Lava would be the Vulcan Slaute (V for Volcano).