Omak Airport

Almost certain just charter flights.

Wenatchee only

Not aware of any flights from omak to Bellingham. Closest would be to take bus to Wenatchee and get a connecting flight to Seattle then toBellingham, otherwise, take the bus, or the train. North 20 cascades pass is closed until about May, otherwise it is a 4 hour drive, 6 hours currently over Steven's Pass and north on I5.

I believe there is a private charter plane that makes regular flights from Wenatchee, 95 miles away, though there is a daily bus service, the Apple Line, from Wenatchee to Omak and all parts going north to Canada on hwy 97, that would be more cost effective. Shuttle flights to Wenatchee from various connecting airports are common.