"For some reason Turbo Tax is generating a Form 8853 in my return."
There are two reasons why this might happen: (1) you checked off MSA on the screen where you checked off HSA, and (2) somebody's W-2 has a code R in box 12 (this indicates contributions through the employer to the MSA). So go check all your W-2s.
"TT then goes into me and asks if I had HDHP coverage as family, self or none. If I select family, the system is telling me I had a gap in coverage. "
This is a problem with the HSA interview. Because you did not have an HSA, you never had a chance to tell TurboTax that you were covered under your spouse's HDHP policy. Basically, this question isn't intended for you.
"What answer should I put for myself?"
Answer NONE the next time you see it.
"How do I get TT to not provide form 8853 since we don't have an Archer account?"
See my first response. Somehow, somewhere, TurboTax came to think that you had an MSA.
If your W-2 has a code R in box 12, then your employer thinks that you had an MSA, so you would need to talk to your employer about a corrected W-2.
Otherwise, you can just go and directly delete the 8853 and see if that fixes your situation.
*** Desktop***
1. go to View (at the top), choose Forms, and select the desired form (8853). Note the Delete Form button at the bottom of the screen.
*** Online ***
1. go to Tax Tools (on the left), and navigate to Tools->Delete a form
2. delete form(s) 8853
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