You can't use money from an HSA or an FSA to pay medical insurance premiums. See publication 969, pages 10 and 18.
https://www.irs.gov/pub/irs-pdf/p969.pdf
Also, you will have to be careful that the plan you select is eligible for further HSA contributions. Once you own an HSA, you can spend the money for any qualified medical expense, but you can't make contributions unless you are enrolled in a qualifying High Deductible Health Plan.
Also beware that if you enroll in an FSA, you will be disqualified from making contributions to your HSA, unless it is a "limited purpose" FSA. Because you can use FSA funds to pay for medical expenses for yourself or your spouse, it counts as "other medical coverage" that disqualifies you from contributing to an HSA. (Except for a limited purpose FSA, see publication 969.)
It's not clear if you mean that you want to move your wife to a private plan, or that you want to both move to a private plan. If you move your wife to a private plan, your maximum contribution limit to your HSA will be reduced from the family level ($7200) to the single level ($3600). If your wife enrolls in a private marketplace plan that is HSA qualified, then she could open a separate HSA in her own name and also contribute up to the individual maximum. (Remember that an HSA is owned by one person only, there are no joint HSAs.)
The only tax break for paying private insurance premiums is the ability to deduct the premiums on schedule A, after meeting the 7.5% floor and assuming you itemize your deductions in the first place. Because health insurance premiums are deducted before federal income tax, state income tax, and before social security and medicare tax, you likely save close to 35-40% in taxes by using an employer sponsored plan. With the limitations on the schedule A deduction, your private policy would have to be 30% cheaper before you could think about breaking even. Are you sure this is the right thing to do?
