As others have pointed out, your question is a bit misleading. "Flow rate" and "filtration rate" are not necessarily synonymous. "Flow rate" usually refers to how much water movement is occurring inside the tank. "Filtration rate" refers to how often the filter is turning over the total tank volume, i.e. how many gallons are passing through the filter per hour.
Filtration of 563gph for a 125 gallon tank might not be enough filtration in the long run as waste loads will increase. You should always set up a tank for its future needs, not for what you are planning on stocking with today. More filtration is always better as you cannot have too much filtration. However, if you don't have a high enough flow rate to move the water and keep detritus suspended, allowing the filter to remove it, no amount of filtration will be enough. I usually shoot for a filtration rate of at least 10x the tank volume and adjust up if I plan to stock with high waste producers (Lion Fish, Puffers, Groupers, etc).
The flow rate should be based on tank inhabitants as well as tank dimensions. A tank that is 72” long will need stronger and/or more powerheads than a tank that is 60” long. Start off slow and work up until you feel you have enough flow. Try powerheads with about a 1200 gph flow…one on each side wall facing each other and position so you get a circular type flow. The 1200 gph is just an arbitrary number. Your tank will actually tell you what it needs based on how well you take care of it and what your maintenance practices will be.
Just remember it’s not an exact science. What works for one person does not necessarily work for another. Regardless of what works, enjoy and have fun!