I have funds in my son's 529 plan. I want withdraw those funds and pay my son's student (Stafford) loans. How do I prove to the IRS the money was used to pay his loans?

You don't have to prove it, at the time you file your tax return.  Proving it comes later, if you're ever questioned by the IRS.  It seems simple enough to do so: loan documents and a cancelled check. 

 You can just not report the 1099-Q, at all, if your student-beneficiary has sufficient educational expenses, including the maximum $10K loan payment. When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms. 

On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution."