Where to start?
First, with a word for “burn.” The most general word is uro; however, in this case comburo (burn up, burn completely) is more fitting.
Next, “shirt” is always a bit difficult to translate, but as you suggested “tunic” yourself, let's go with tunica. (Attempts to find a more accurate translation usually concentrate on the “undergarment” aspect, but I doubt you're all that interested in that.)
Now we just take the imperative form of the verb, put the noun in the accusative case, add a demonstrative adjective, and we get:
Combure istam tunicam.
Where English has “this” and “that,” Latin has a somewhat confusing selection of is, hic, ille, iste. I chose iste here, which we generally use when referring to something that is closer (in mind or in reality) to the listener than the speaker. “Burn the shirt you are wearing” sounds like that would be the case. Although I would really expect to hear “Burn that shirt” in that case. “Burn this shirt” sounds more like the motto is printed on the shirt, in which case you would say:
Combure hanc tunicam.