This is a (hopefully tongue in cheek) representative of the sacred-profane dichotomy! This is still hard to answer but here's some thoughts.

So this is Durkheim's thing so think of "God" as a mythological metaconcept. This is more sociology than proper theology, but it's the only thing I can think of that's relevant. God, in this way of thinking, is what emerges when cultures uplift their ultimate concerns over time. "God" would be a collective concern of the highest priorities of people. So, prayer is accessing "God" or the sacred.

Farting is the profane. It is a mundane, collectively frowned upon, aspect of your living.

So, farting while praying is an overlap in what is traditionally dichotomized. While traditionally dichotomized, there is increased thought on God's immanence -- God in the here and now, the sacred in the profane. There have also been responses against this that reemphasize God's transcendence -- the sacred-profane dichotomy reemerging. A one size fits all answer isn't present, even on an abstract level, so getting to the rubber meeting the road of praying and farting is difficult.

Process theology, sacramental theology, and pan(en)theism will further the discussion of God's immanence / the sacred in the profane whereas a lot of more traditional theology will dichotomize them.

Think on how much God is active in day to day life, in the world. If you tend to take God as more transcendent, you're likely dichotomizing the sacred and the profane so farting during prayer is a no go. If you see more of God in the day to day, in the world, then you likely have an understanding of the sacred in the profane.