My son is 8 now and has always lived with me, his mother left the household when he was 3yrs old. She sees him a couple times a week, but most of the time they are at her parents house (visitation not court ordered). I now want to move the state due to a great opportunity, she is threatening to take me to court and report a kidnapping, he doesn't live with her, I have all his personal paperwork, I'm the parent on the school contact, I provide health insurance. Can I move states? Will the court give her custody? What rights do I have?

No, you have no legal rights to move, unless the court has approved.

What I did not hear, do you have legal custody, though the court?

If not, the mother can just merely keep the child one time. And not give child back.
Without court order, she has the same rights as you do.

Have you ever been to court for custody at all? Are you at this time the legal father?

First, any question on law needs to include your general locale as laws vary by area. Second, as noted, we need to know if you are the legal father, are you on the birth certificate or do you have an acknowledge of paternity signed by both you and the mother or were you married to the mother at the time of his birth? We also need to know has anything been done in court regarding custody, visitation or support at any time?

Assuming you are the legal father and that there are no court orders awarding custody or visitation, then either of you has full rights to the child. She cannot charge you with kidnapping unless you hide from her. If she goes to the police to do so, they would ask for proof that she is the primary custodial parent. Without that proof they will not pursue a kidnapping charge. But she can go to court and gain custody. If you move without court approval, she can get a court to force you to return the child.

So what you need to do is go to court, establish yourself as the primary custodial parent and get the court's permission to move. This will probably involve a compromise on your part in allowing her visitation on holidays, summer vacations etc. at your expense. I would strongly suggest retaining an attorney.