If mixing baking soda and vinegar in a drain pipe clears the clogged drain, then I expect it's all the CO2 gas produced that does the trick.
My sister swears by a product sold here in Canada called One Second Plumber. Basically, all it is is a can of compressed air.
You simply place the can upside down over the drain with the yellow foam rubber cone forming a seal, and push down. The can blasts compressed air into the drain pipe and clears the clog right away.
I'm thinking that if the relatively slow rate at which mixing vinegar and baking soda produces CO2 gas is effective in clearing clogged drains, you might want to look for One Second Plumber for sale in your area and give it a try.