How do I go about expungeING my military record?

I don't believe you can expunge a military record.

Not possible to expunge, you need a pardon.

You would have to hire a lawyer and go to Federal Court.

I will assume you mean a criminal charge (not your entire military record)
Normally it is not done, and as noted a Federal pardon would be needed.
If at all possible, normally it could only be one charge, and a lawyer is needed since it has to be filed within the military justice system. Military court.

But even that will still show up on higher security background checks.