I currently have Tricare Reserve Select and a separate FSA as part of my airline pay. Haven't had any issues so far.
You are correct about the HSA. HSAs require a "high detectable" Health Plan.
Good luck!

"Qualifying for an HSA

To be an eligible individual and qualify for an HSA, you must meet the following requirements.

You must be covered under a high deductible health plan (HDHP), described later, on the first day of the month.

You have no other health coverage except what is permitted under Other health coverage , later.

You are not enrolled in Medicare.

You cannot be claimed as a dependent on someone else's 2015 tax return."

https://www.irs.gov/publications/p969/ar02.html