Sure, your own property. If I burn your flag, you can stop me. If I burn my own flag, you have no right to interfere with my destruction of my own property.
United States Code
TITLE 18 - CRIMES AND CRIMINAL PROCEDURE
PART I - CRIMES
CHAPTER 17 - COINS AND CURRENCY
§ 333. Mutilation of national bank obligations
“Whoever mutilates, cuts, defaces, disfigures, or perforates, or unites or cements together, or does any other thing to any bank bill, draft, note, or other evidence of debt issued by any national banking association, or Federal Reserve bank, or the Federal Reserve System, with intent to render such bank bill, draft, note, or other evidence of debt unfit to be reissued, shall be fined under this title or imprisoned not more than six months, or both.”
You own your money too.