Whenever you start walking your digestive system gets moving and trapped gas in your stomach also moves through your stomach and digestive tract as well.
So you already have the gas built up in your stomach and intestines but your body then moves the gas in your stomach.
So when you walk then you start farting and I sometimes get that farting when walking myself and it can be embarrassing but a lot of other people fart when walking as well.
It's nothing to worry about and means that you're just more gassy than some other people.
I've read online before that when you have gas built up and trapped in your stomach walking helps to get the gas in your stomach moving around.
Then that gas that was trapped in your stomach gets relieved and removed from your stomach because you're farting.