A servicemember separating from active service may be eligible for unemployment compensation under the Unemployment Compensation for Ex-service members (UCX) program. However, if you are getting separation pay, the unemployment amount may be affected. And if you take retirement pay, you are also eligible, but may not get any unemployment since the retirement amount is probably greater than the unemployment amount. Every state administers this in a different way, but check on it anyway.
Now, if you are retired military, get a job at an airline, work there for a year let's say, then get furloughed, you should be eligible for unemployment just like any civilian worker who gets laid off.
In all my years representing unemployed clients, I have had very few retired military even with the proximity of Fort Lewis and McChord AFB, and those were limited to issues on re-training instead of eligibility. This one client had been manning a machine gun or something, and obviously could not find a similar job in the civilian world. He wanted to retrain as something else, but the question was what. I still think about him.