Kim Zolciak Breaks Down Onstage While Talking About Kroy Biermann Divorce

kim zolciak kroy biermann Kristin Cavallari getty handout composite

Kim Zolciak's relieved she's "finally free" from Kroy Biermann ... breaking down onstage while talking about her divorce -- and, clearly she feels like she's been under immense pressure.

The reality television star appeared at a live taping of a new show Kristin Cavallari is landing with NBC ... and, they dove into Zolciak's divorce -- the first time KZ's really sat down and discussed it.

talking it out

While we don't have video of the two diving deep into it ... sources at the event tell TMZ they chatted for a good 20 minutes about the topic -- and, at one point it got super emotional.

Sources tell us Kim broke down in tears…