Based on the history of the Amazing Race, the logical flights are AA169 and UA891 as outlined by Chateau. However, those are not the only possiblities in the approximate time frame.
There also was :
KE002 11:40 - 15:05
NH005 12:55 - 16:20
NW001 12:55 - 16:20 (note: NH005 may be a code-share of this)
JL061 (code-share American and Delta) 13:20 - 16:45
The next flights do not leave until 1445, almost 1.5 hours later so I think the above are what makes sense.