I don't know you're within a block of the Light Rail station which goes to SeaTac. Don't know when you'll be arriving or how much time before your flight but it's doable and walkable. If you go on the Seattle forum and look on the top right under top questions you will see a detailed question on getting from Amtrak to Sea-Tac using light rail. Cabs would be a flat $40 or Uber or Lyft would be a little bit last?
Yes, from Amtrak station walk to International District Station - it is a short 5-6 minutes walk. From there you take the Light Link rail which will take you to the airport.
Note: you need to pay before getting into the rail.
You can find detailed schedule here:
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