As CX500T said, you'll be fine.

Nothing special or different at all related to being foreign or green card. UK isn't very foreign by our lights anyway.

You'll have a leg up based on the military background. If you don't have a college degree that may be a factor (essentially all US mil pilots do), but it's not required any more and I think the mil background will supersede that anyhow.

Just focus on getting your flight credentials competitive for your end goal, the rest is non-issue.