2006 Chevy Silverado Transmission flush and synthetic fluid

I just purchased a 2006 chevy silverado 5.3 liter flex fuel ready. 84,000 miles very well maintained from the looks of everything, but I do not have prior service records.
I wanted to know if I could do this:

I would like to flush the transmission with a quality synthetic transmission fluid and change the filter. Then drive for about a month or 1000 miles, and then do a fluid and filter change. (Not a Flush using synthetic fluid again.) I have read that when you flush a high mileage tranny that the synthetic fluid can breakdown any sludge or buildup and cause premature failure of the filter. So I will only go 1000 miles or 1 month and then just do regular fluid and filter changes from there using synthetic fluid for the life of the vehicle. How does this sound to you?