My son's biological father has been in and out of my son's life for almost six years. I filed for custody and won with visitation at my discretion. His father is in and out of jail on a regular basis. I can not get him to give up his rights, he won't do it because of his ego "what will people think if they know he did that." He was 5000 dollars backed up in child support which he only paid to get out of jail. He is not paying again. I need to know how long does my son's biological father has to be out of his life before my husband can adopt him without the biological father's permission or signature saying he agees

In most states this is not a clear cut answer in some, he will almost always have to give him permssion or be where he can not be found.

In others he can lose his rights after a period, but not for adoption.

So basically it will normally just be up to the judge, if he does fight it.
In all cases he will have to be notified and have the right to present his info to the court. Also since he is paying child support, even if it is to get out of jail, then he is doing some of the court ordered items

Terminating parental rights, especially involuntarily is an uphill climb. It is rarely granted. The fact that you want it done to permit your husband to adopt is a point in your favor. But if the bio father does not pose a danger to the child and refuses to relinquish, there is probably not much you can do.