The dishonorable discharge is based on a general court-martial conviction. This means the conviction is a felony, regardless of what the underlying offense may have been. The convicted felon is banned from possessing a firearm including Title II Firearms (a Silencer, SBR, SBS, AOW, or Machine Gun).
A person who is convicted of a crime that is punishable by imprisonment for more than one year ( including a dishonorable discharge) is prohibited from possessing a firearm. Under 18 U.S.C. 922(g), a felon who is found guilty of gun possession may serve up to 10 years in prison.
If you have been convicted of a felony or a dishonorable discharge, be careful of constructive possession. You could be guilty of being in possession of a firearm if your spouse or another family or household member has a firearm that you "could" access.