Should an Officer who was non-selected for promotion, and discharged at 16 years of service, reenlist to finish their 20?

I can't imagine why he wouldn't

It depends on your life circumstances. I have seen several do it. Another option is to consider applying to become a Warrant Officer, but the potential for that would really depend on what branch you are as an officer.

Officers are not 38B. 38B is the enlisted MOS for civil affairs.

You should go full time reserve or national guard for four years the retire.

Had a friend who was an Air Force Lt retired SFC. Another associate of mine was an Air Force Pilot (Major) wearing his wings as a Army Sergeant to finish his 20.

There were many officers who did this after they were riffed at the end of the Vietnam war. I had one friend who had been a Marine Corps Captain, who made it to SGM as an EM. But his CPT retirement pay was still higher.

16 YEARS Invested, And That's A Question?
UH ~~ Well Oh "L" Yes!

UH,,,, YA!!
Ya THINK....??
That Question Falls Into The Classification Of
~ "DUH" ~

Check with the in-service recruiter to see if you are eligible to re-enlist active duty. If you can, then enlist for 4 years to complete your 20. You should be dual component with your active duty enlisted rank, and also in the inactive reserves at your commissioned rank. Key thing to do is get with your CSM to see if you can be boarded for the next rank before you leave your unit. Otherwise, you may find the new post has a bar to enlistment all prepared when you try to inprocess.

If you are eligible to enlist (not re-enlist) you likely could get the MOS for a Chaplain's Assistant since you are a Chaplain, unless your non-promotion was due to the loss of your church's endorsement. Good luck.