At termination, the value of the FRA is V = [(r - fixed rate)*fraction of year]/(1+ r*Fraction of year) and r here is some forward reference rate.
That means the value of the FRA now is V*Exp(-r1* t) where r1 is the rate from now until termination of the FRA. But duration is all about parallel shifts in interest rates so a change in r is the same as a change in r1. So now you need to calculate dV/dr and you're rolling...