There is nothing specific about having a continent pouch and enjoying a hot tub that you should be cautious about for yourself. Talk to all the doctors you want, but the risk is mostly to your skin (skin infections), not your internal organs. You can get diarrhea if you drink the contaminated water. Just like anyone else, you want to get into a sanitary hot tub. I have been in oodles of hot tubs since my surgery in 1995. Never had a problem (yet). Granted, I have a regular j-pouch, not a k-pouch. You cannot stop living your life because of your surgery.
However, you want to be sure that you protect others from infection from YOU! I am not implying that you would leak into the hot tub, but anyone with an ostomy should take care that their stoma is well sealed before entering a hot tub or a swimming pool.
Jan