One component of many employment benefit packages in the U.S. (I don't know about other countries) is a Medical Flexible Spending Account. At the beginning of the plan year you choose an amount to set aside from each paycheck which goes pre-tax into an account, the contents of which can be used to reimburse medical expenses. Depending on your tax bracket, this is equivalent to getting a 20-35% discount on your medical bills.
These accounts show the many fingerprints of bureaucracy. Contribution limits are stiff, often both a percentage of pay and an absolute maximum (current $4K, I think). There are, as one might expect, curiosities to the restrictions on what the money can be used for. Health insurance premiums are not coverable, but co-pays and co-insurance are. Both the basic eyeglass frame and the Elton John special are generally reimbursable. A periodontal visit is reimbursable, but the dental floss which might prevent or moderate that visit is not. In general, you must save all your receipts and then send them in to the plan operator. Some offer a handy debit card that works with one of the credit card networks, but if you spend on anything out-of-bounds you'll need those receipts to sort it out -- and you may need those receipts in any case. Lots of paper to save.
But perhaps the most burdensome requirement is use-it-or-lose-it; any money not spent by the end of the plan year is forfeited to the plan operator. Over the last year or so the IRS has loosened this restriction to allow some overlap in plan years, but not all plans allow such. So, you must carefully plan your expenses or the whole benefit is lost -- or worse. And, should you wish a mid-course correction, that's generally not allowed -- you can't change your contribution event unless something big happens, such as the addition or subtraction of a family member (the former is hard to plan precisely, the latter should never be planned!).
So, around this time companies offering covered items start urging folks to check their account balances and spend them before they lose them. Eyeglass merchants are at the head of the line, but so are laser vision correction places.
Which leads to the title question: can you use MedFlex account funds to pay for DNA testing? I honestly don't know, and really nobody lacking a tax law specialty has any business answering the question. But, if I were running one of the personal genomics startups out there I'd be finding out the answer. Perhaps a precedent has been set for other diagnostic procedures not (yet?) well recognized to be of medical value, such as the full-body scans which were heavily marketed a bunch of years back. For if these funds are available, then that is a ready pot of money which might be spent. One big ticket receipt sure wouldn't be a pain to submit, and if the companies were clever they could split the bill over two fiscal years (say one covering the scan and one the counseling) to enable two plan years to be charged with the expense. I don't know whether it would make good medical sense to have such a scan, but some folks on fence might be swayed if they could see it as a bargain.