I don't know what the flow rate needs to be through the bog to allow it to work properly.
There isn't really a max flow rate, the bacteria can handle high flows, like water in a rushing stream. There is a limit of how much water can make it thru the gravel. Too high a flow and you'll see water bunching up here and there on the surface. The only down side to that is water on the surface generally grows string algae. String algae in a bog is good for water quality but makes a mess if in with plants.
600 gph thru a 12"x12" gravel channel would be no problem.
BTW, water bunching on the surface is also a sign of the gravel clogging. In your case, with the designs in my picture, I wouldn't expect that to happen for 15+ years if plants are kept in pots. Planting directly in the gravel might speed up future clogging, but I wouldn't let that stop you if you wanted to plant directly into the gravel. Clogging is feared more than it should imo.
Water bunching on the surface when you first install the bog just means there's too much water in the bog. If you have an auto fill it means it's too high. Or you just don't have enough gravel in the bog.
You do want the sides of the bog to be at least 1" above the gravel so if any clogs form the water can still flow over the surface and not leak over the side. Easy to test...just over fill the bog with water to check a 1" depth. If the bog overflows before the 1" depth you just have to remove some gravel in the high spots.
The dirt on gravel is not good for the fish and can make a mess of the pond. When you first fire up the bog the water will be very dirty. Pump that dirty water into the yard, not the pond. Keep hosing down the gravel and pumping out the dirty water until the water is clear. A lot of the dirt on the gravel will just wash off and settle on the bottom of the bog where it isn't a problem. When the water is clear you can pump water into the pond after dechlorinating the water in the bog if you have chlorine.
I was thinking a 600 gpm pump in the pond itself moving water around and a 600 gpm to move water from the bog sump at the end back to the pond. Does this make sense?
I don't know how big your pond is or number, kind, size of fish, or how much food you feed, so I can't say on the amount of flow exactly. But going by the photo you posted those pumps sound very good.
If it was me I'd probably just have a single 600 gph pump in the bog and have the out flow in the pond about 1' off the bottom so the water in the pond rotated. If I had two pumps, or I wanted two pumps as backups to each other, I would put both into the bog and run 2 out flow pipes into the pond. That gets you even more rotation, more O2, more water in the stream, more water thru the bog.