http://www.atf.gov/firearms/faq/licensees-conduct-of-business.html#out-of-state-resident
Q: May a licensed dealer sell a firearm to a non-licensee who is a resident of another State?
Generally, a firearm may not lawfully be sold by a licensed dealer to a non-licensee who resides in a State other than the State in which the seller’s licensed premises is located. However, the sale may be made if the firearm is shipped to a licensed dealer whose business is in the purchaser’s State of residence and the purchaser takes delivery of the firearm from the dealer in his or her State of residence.
In addition, a licensee may sell a rifle or shotgun to a person who is not a resident of the State where the licensee’s business premises is located in an over-the-counter transaction, provided the transaction complies with State law in the State where the licensee is located and in the State where the purchaser resides.
[18 U.S.C. 922(b)(3)]
http://www.atf.gov/publications/download/p/atf-p-5300-5/atf-p-5300-5.pdf
Washington regs: 9.41.122. Out-of-state purchasing Residents
of Washington may purchase rifles and
shotguns in a state other than Washington:
PROVIDED, That such residents conform to the
applicable provisions of the federal Gun Control
Act of 1968, Title IV, Pub. L. 90-351 as administered
by the United States secretary of the treasury:
AND PROVIDED FURTHER, That such residents
are eligible to purchase or possess such weapons in Washington and in the state in
which such purchase is made.
http://www.atf.gov/publications/download/p/atf-p-5300-5/atf-p-5300-5.pdf
Texas regs: 46.07. Interstate Purchase A resident of this
state may, if not otherwise precluded by law,
purchase firearms, ammunition, reloading components,
or firearm accessories in contiguous
states. This authorization is enacted in conformance
with Section 922(b)(3)(A), Public Law 90-
618, 90th Congress.
You are GTG.. I found nothing indicating a lower receiver being anything different than a long arm.
The way I see it, you show up, present your WA ID and make a legal purchase.... no military credentials or " orders " are required.
If you are flying back, check it in - as you would a complete firearm.
Have Fun
ETA: More stuff... " ATF FFL Quick Reference " ... I'll skip the " And Best Practices " BS -
http://www.atf.gov/publications/download/p/atf-p-5300-15.pdf
Permitted Sales to Non-Residents of Your State
You may sell a firearm to a person who does not reside in your State by shipping the firearm to a licensed dealer in the buyer’s State of residence and having the buyer take possession of the firearm from that licensee. The licensed dealer in the buyer’s State of residence is responsible for the Form 4473 and NICS background check. Your A&D records should reflect the transfer to the out-of-State FFL and not to the end purchaser.
You may make an over-the-counter sale of a rifle or shotgun to a non-resident if the transaction complies with all the laws of your State and the laws of the buyer’s State.
The way I do it, if the dealer has any problems, have him pick up the phone, and call the 800 number.
You now have the references to the links above.