There is no denominational policy concerning the use of flags, including national flags, in the sanctuary. According to Rev. Dan Benedict (director of worship resources with Discipleship Ministries from 1993-2005), "There is no place in our hymnal or Book of Worship, which contain our United Methodist ritual, where there is even a suggestion of bearing the flag in procession, saluting or pledging allegiance to the flag, or that the American flag should be in worship." So, nothing requires it. And the absence of such directions including a flag seems to downplay such a role.
The Scouting Ministries office of the General Commission on United Methodist Men, "encourages the use of flags in some special services, such as Eagle Courts of Honor and other events that have both a civic and a religious element when they are 'sponsored' by the local church. The Christian flag reminds us of our faith. The American flag reminds us of our heritage."
For more on this topic, watch this video from Liturgy Man, or read this blog on the same topic.