What is the ruling on one who suffers from frequent flatulence and urination almost constantly due to irritable bowel syndrome, and how should one deal with that before prayer?

Unintended release of gas places you in the category of one afflicted with perpetual ritual impurity (sahib al-salas). You should perform ablution after the time for prayer begins and then pray as much as you wish until that time expires. As for frequent urination, one should relieve themselves before prayer to avoid needing to use the restroom during it. It is also advisable to consult doctors.