Yes, in a quick re-read, I can't find if the OP's pool is IG or AG. His concern about how much to empty led me to believe it is IG. Which inspired my comments. Pardon if I got that wrong...
s_vidden, your comment about not needing a flow meter and determining the amount of the exchange with dimensions makes sense if the OP is going to drain and refill. If he's going to exchange as I suggested, I think he would need a flow meter, at least to get close. His water level won't be dropping, so there's nothing to measure! The exchange won't be exact, and some mixing will occur, but a flow meter would keep him in the ball park.
Good news, rob42, whether you need one or not, you've probably already got one, if you're on metered water. You can use the house meter out by the street. Impose a ban on showers, laundry, dishes, etc. Go out to the street and take a picture of the number on your water meter. Start the exchange and keep an eye on the meter for when you hit your mark. The picture is in case you forget the starting number (something I would do in like five minutes!!).
You'll be hopping back and forth to maintain the water level and eye the meter. Balancing water being siphoned out vs water coming in. Then checking the meter for your target number (determined with a little math, adding the desired gallons to exchange to the original meter read). EZPZ. Meanwhile, the rest of the family will be lounging inside because they've just been given the day off: no laundry, no dishes, no washing the car, etc. It's a win-win!!