User blog comment:ChishioKunrin/Taiyang got a tattoo/@comment-26397825-20151027114325

A pair of dragons fits with their last name, and it could be a more permanent identifier instead of just a piece of cloth or metal with his symbol (if it is indeed his symbol and not just something he got for the fun of it).

The burning heart aspect could also be a homage to something in the Xiao Long family tree - kind of like the Schnee's have a snowflake, but I'm sure every individual Schnee has a variant on it.