If you do, you may be in violation of RCW 9.86.030:
(1) No person shall knowingly cast contempt upon any flag, standard,
color, ensign or shield, as defined in RCW 9.86.010, by publicly
mutilating, defacing, defiling, burning, or trampling upon the flag,
standard, color, ensign or shield.
(2) A violation of this section is a gross misdemeanor.
The law specifically protects the US and Washington State Flags, but not the Oregon Flag. This law was passed in 2003 as part of a general reorganization of criminal law. Although there was a case in 1970, State v. Turner which impinged on that statute, the Washington Supreme Court has not held the statute unconstitutional, to the best of my knowledge, and SCOTUS has not addressed the case either. I don't know, perhaps some prosecutor would be willing to put this to the test. The court in Turner seems to have signalled a willingness to uphold the law in case the flag burning was part of an incitement to violence.