It would be risky doing just a regular flush with stock pump when water has been mixed with the trans fluid. Once you have had the truck running and water gets mixed with that fluid it separates and becomes bubbly or air raided. A machine would be best to get all the water out and maybe even less costly. Mainly bc it may take a few times and a lot of new fluid to flush out all the water from the left over fluid even after you drain it. Most shops may even go to the route of changing all associated parts before doing the trans flush just to avoid any problems. If I did this at home or personal garage I personally would drain trans, do a flush once, then replace all lines, blow out as best you can from the radiator, if you have a trans cooler then replace that and then replace filter and then not sure on your vehicle or any of the newer ones for that matter have it, but drain the torque converter if possible. You can run the truck a little to see if anything comes out of the return line after you drain everything but like stated above not for too long at all, you could burn up the pump, then after that add fluid and do a trans flush with the stock pump again and keep adding fluid while your watching it come out of the return line. Like I said with stock pump you may have to do this a few times or keep adding more and more fluid to get all the air-raided fluid out of the trans and torque converter(if you can not drain it).
Best rout though is to get a shop with a machine.