My father was in WW2. He was an instructor to new cadets, teaching
them how to fly. He died recently, and was buried with full military
honors. His wife is living, but has Alzheimer's so bad she wouldn't
know what was going on if she was presented the flag. So her
grandchild,(not my father's flesh and blood), was presented the flag.
My sister and I were there, but we did not make the funeral
arrangements. My father's wife's daughter made the arrangements. She
never asked us about the flag presentation, so it was a shock to me
and my sister that the wife's grandchild was presented the flag,
rather than me, his only son, or my sister, the oldest daughter. Were
we entitled to receive the flag, or does his wife's side of the family
get it?   Thanx, Michael at  m.f.b@cox.net

Hello.

The rule is that the flag goes to "primary next of kin" (PNOK).

"h. Flag and Flag Case. A flag of the United States, with plastic flag
case, is authorized for the primary next of kin and the parent or
parents of the deceased military authorized for the primary next of
kin and the parent or parents of the deceased military member (if
parents are other than primary next of kin).
(1) Next of kin flag. The next of kin flag is used to drape the casket
at the funeral home and during interment services. After interment
services, the flag is folded, placed in the flag case, and presented
to the primary next of kin.
(2) Parent's flag. When the parents are not the primary next of kin, they are
authorized to receive a flag and flag case. This flag may also be
presented at the interment service or if they are not present at the
interment, it is mailed to them."
source: 
US Army - Lesson 6 - Disposition of the Deceased
http://milmed.pmk.ac.th/md0755%20PATIENT%20AFFAIRS%20BRANCH.pdf
(This document is in PDF format, so the Adobe Acrobat Reader is
required. If you don't have that, visit:
http://www.adobe.com/products/acrobat/readstep2.html )



The Primary Next of Kin (PNOK) line of succession is as follows:

(a) Spouse.
(b) Sons or daughters in the order of seniority.
(c) Oldest parent unless legal custody granted to another person.
(d) Blood or adoptive relative granted legal custody.
(e) Brothers or sisters in the order of seniority.
(f) Oldest grandparent.
(g) Other relative in accordance with laws of deceased's domicile.

source: 
US Army - Lesson 6 - Disposition of the Deceased, p. 6-10
http://milmed.pmk.ac.th/md0755%20PATIENT%20AFFAIRS%20BRANCH.pdf

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search strategy:
"military funeral" flag
flag  "primary next of kin" oldest 

I hope this helps.

Although realistically, the officer on the scene will usually do
whatever he is told to do by the family as a sign of respect.