If a person suffers from uncontrollable gas he should at least wear tallis and say Krias Shema within the time. Whenever he will be able to wear tefillin in the day he should put them on. Better to allow zman tefilla to go past and daaven twice Mincha if he knows he won’t be able to daaven Shacharis with a guf noki. (ShA – MB 3,4)
If he thinks he will be able to control from passing gas for enough time it takes to say Krias Shema and tefilla he should skip everything else and at least say those. (MB 2)
Similarly, if he thinks he can control himself during Krias Shema – he should place his tefillin on between Ahava Rabba and Krias Shema and remove them immediately after Krias Shema. (ShA – MB 4)
If this illness is chronic, he should daaven as usual just make sure to stop daavening until the gas smell dissipates. If he can manage to stop the gas just to put on his tefillin shel yad, he should put them on one by one without a beracha and take each off immediately. (MB 4)
If a person has a sickness that causes uncontrollable urine flow, he should wait – when the dripping stops he should begin tefilla and pause only when he feels it dripping. He should wear something underneath to absorb the urine so that the outer garments stay dry and clean. (MB 4)