I empty my pouch 6 to 8 times per day and I drink 10 to 12 cups of liquid. I drink tap water (easier). I don't use a syringe as I found that the rubber degrades over time so I started to use a disposable enema bottle. I dump out the contents and then rinse out the bottle. When I flush the bottle doesn't totally empty so after I remove the catheter I use the remaining water to flush out the catheter. The bottle is about 4.5 oz so I suppose when I flush it's about 3.5 to 4 oz and as I said I use the remaining 0.5/1 oz left to rinse out the inside of the catheter.
I flush after every time I empty my pouch. Since the enema bottles are over the counter item I don't submit the expense to my insurance (but then I don't submit any of my k pouch expenses). But the enema bottle are easy to obtain. I don't have to order special and can go to most stores and purchase them. If you look online you might be able to get a deal. I've gotten them at the dollar store and grocery store. I've paid around $1.00 for each bottle. Sometimes less.
Good luck.