While there may be several causes of the imbalance that causes indigestion, one of the common bacteria that get out of balance in the stomach is Helicobacter pylori.  Common medical treatments for that imbalance are over-the-counter prescriptions aimed at reducing stomach acid or antibiotics that kill all the natural flora.  The antibiotic route, while effective at reducing the number of H. pylori, also kills all the bacteria that keep digestion going smoothly.  That sort of throws the baby out with the bathwater; natural levels of bacteria are essential for digesting proteins and complicated carbohydrates.

Kefir is a pro-biotic rich milk product that has been used for generations as a broad spectrum, nutrient-dense superfood.  A recent study looked at the benefits of kefir when used in conjunction with traditional 3-plex antibiotic treatment for patients with reflux and indigestion.  The researchers took measurements of urea in the participants' breath and looked for both a drop in urea levels and an improvement of symptoms versus the 3-plex and a placebo.

Kefir was overwhelmingly successful.  78% of people given the kefir mixture completely eliminated urea from their breath test as opposed to 50% in the placebo group.  Probably as important, the side effects were much less in the kefir group since it helped establish balance in the natural flora.  

Onder Bekar, Yusuf Yilmaz, Macit Gulten (2011). "Kefir Improves the Efficacy and Tolerability of Triple Therapy in Eradicating Helicobacter pylori."  Journal of Medicinal Food 14(4): 344-347. doi:10.1089/jmf.2010.0099.