Flag burning is a symbolically charged action, usually associated with rage or hatred. Given the attachment to what people feel to a flag which (they feel) symbolizes their identity, it would be entirely reasonable for a gay person to conclude that the church hates them.
Flag burning, Quaran burning, Bible burning, effigy burning, riots, stupid signs is more within the playbook of the Westboro Baptist Church and IMO has no place in a church such as ours that is built on and prides itself (mostly) on its rational and intellectual heritage.