Following prescriptions for neck injury/migraines, a relativehas become addicted to prescription painkillers. What is thebest course of action to end addiction?

Pain specialist. This is not uncommon, and likely very unnecessary. You should find a doctor who specializes in trauma and pain management, and get either detoxified or under better control. There may be issues such as crps that need to be addressed. Seek additional help.
Detox. If the person is aware of his problem, and would seek help, guidance is needed to be admitted in a detox facility as the first step. A psychiatrist may help you if there is no insight into it, as well as family interventions. You can call 1855-detox-00 or aa/na hotlines for further info. Rehab and na meetings are customary after the detox process. Good luck !
Pain medications. Chronic pain medication usage can become a serious issue in terms of addiction, dependency and tolerance. Your relative has a neck injury, but does this neck injury constitute any cervical disc herniation or stenosis. If yes, then surgery would be considered as a last treatment option. Chronic use of pain medication will never resolve the pain and addiction issues. Best regard.
Careful evaluation. The first thing i would recommend is to be sure your relative is indeed truly addicted to painkillers. He or she may very well be addicted: dysfunctional behavior, craving pain medications, withdrawal symptoms, lying, worsening side effects, and so on. Or, he or she could be appropriately dependent on the pain medications because of severe chronic pain. It's difficult to tell the difference.