Allowed, yes. Wise - possibly not.
If you contribute to the HSA through payroll, you usually will save FICA in addition to income taxes, so that's 7.65% in extra tax savings you're leaving on the table unless you're over the social-security maximum.
All you have to do is keep all of your contributions + any employer contributions under the allowed maximum - you can fund any number of HSAs, so long as the total is under what you're allowed.
No idea what BOA loyalty benefits are worth, but be sure you know the full extent of the trade-off and act accordingly.