Who is considered the next of kin?

Generally: Wife, then children, then parents in that order.

Your question may be best answered by contacting the family support services of the military installation that is supporting the funeral detail. There may be a specific military regulation or directive on point. Under Alabama law, the determination of "next of kin" in general terms is decided under the Probate Code. The surviving spouse is considered the closest relative. See, Code of Alabama, 1975, section 43-8-41 concerning intestate distribution. In Code of Alabama, section 43-8-42, if there is no surviving spouse, the estate passes to the children of the decedent, but if no children, then to his/her parent or parents. After that point, the Code specifies other relatives by degree of relationship (referred to in law as "table of consanguinity").