Your cost basis would be your relative's basis (probably the original purchase price) if the basis is equal to or more than the current value of the gun. I assume that is the case if it might have been an antique. In other words, if you sold for a profit, use your relative's cost.
If the gun was worth less than your relative's basis—and you sold at a loss—then use the FMV. However losses are not deductible on sales of personal property.
The loan complicates things. If the gun was repayment of the loan, the donor sold you the gun for the loan amount, so that would be your basis.
The IRS has a more complete explanation at What is the basis of property received as a gift?
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