If you are after a Flat hotel, it may be helpful to know that Expedia's booking site of lodgings in United States of America doesn't include lodgings in Flat itself.
Why not see some more of the mountains and tundra that are commonly found in in Western Alaska? Opt to spend a few extra nights in other parts of Western Alaska. Whether you join in with the common regional activities, for example cross-country skiing, or just tour around to explore the area's offerings you will be able to reserve suitable accommodation in the vicinity.
Now that you've learnt a little about hotels and apartments options in Flat, be sure to check out Expedia's Flat travel guide for all the latest on things to see and do in this area.