Unpredictable chance. There are a number of addictions that have tendencies to be inherited in varying degrees. There is no evidence that sexual addiction is one of them. That said, the presence of addicted individuals in a family does suggest others there are at risk of becoming addicted. Reasons for that are multiple including genetics as noted, broken families, severe financial stress and trauma of all types.
They are increased. Compulsive sexual activity is often a form of addiction which has combined biological and psychological roots. Your children may inherit biologically an decreased capacity to sooth themselves in other ways. Because you don't have this capacity you may find it hard to teach it to your children, and so pass it on psychologically.