How do I get my family member's incompetent papers reversed and have him declared competent?

I'm assuming that this is a guardianship situation & you want that dissolved? I've not been a guardian/conservator but have been an executrix twice and spent more hours in probate court where G/C are heard. Here's my take - once a G/C is done it is rare to be changed as its a pretty involved legal process to get a G/c in the first place. Judges aren't keen on reversing themselves either. I saw it done couple of times - changing GC to another family member due to deployment & rescind of GC due to change in medical condition as they were off chemo, recovered & cancer free so there was MD letters attesting all that and the person appeared in court and totally normal & answering judges questions & the current GC was totally kum-ba-ya in all this. The current GC should have a final report at the ready done to present the judge too.

Your person will have to appear and show ability to the judges satisfaction & have medical or other items to counterpoint why the situation has totally reversed itself.
It won't be simple. Good luck.

You go see an attorney who can interview you and the person in question, then offer an independent, impartial opinion on whether this is feasible. In most cases, dementia does not reverse itself.