I think both gulping and indigestion could contribute to excessive flatulence (passing gas). Indigestion, food intolerance or some other cause for GI imbalance is likely the biggest factor, though. Especially if the stool is sometimes abnormal.
You might try hand feeding her, one kibble at a time, having her sit and wait in between each bite. This will prevent the gulping and help with self-control and bonding to you. If you try this for a week or so and the gas is still a problem, you might think about trying some different dog foods.
