Although I was also confused at first, now that I know the real question I still don't completely understand why it's being asked.
You are a CFI. You haven't done FRs for a while. But you ask what you should charge for the flight portion of a FR?
Since you're interested in the rate for 1 hour of flight, you don't seem to be interested in the "flat rate" method. So, why would you charge anything other than your regular hourly rate?
A one hour flight is going to of necessity require probably 1.5 hours of your time at a minimum, so the minimum charge would be 1.5x your hourly rate. Or, if you prefer to only charge by flying time (boiling in your ground time into the rate), then you're looking at 1x your hourly rate.
If you're just asking what you should charge as a reasonable hourly rate in your area, really they only way to determine that is through a market study - call the local flight schools, call independent CFIs and see what they charge. Unless of course you have a specialty that can command a higher rate.
As for me with FRs (when doing the full thing, ground and flight), I don't see any real way that doesn't turn into being together for about 3 hours, so the "minimum" charge would be 3x my hourly rate. But if everything goes perfectly and it's only 2.5 hours, then they of course get charged 2.5x my hourly rate.