The Briar app seems, unfortunately, saturated with memory leaks of some sort. It seems that the more data you have in the app, the more likely you are of experiencing an OOME. I can produce an OOME consistently by opening and closing private groups, ~20-50 times, I've got 6 groups with different amounts of data in them. I feel this gets worse when more data is added to a group/more groups.
This problem is not only bound to the private groups though, during our extensive tests yesterday I experienced this in other parts of the app (don't remember which though). Note that I did not rotate the phone at all, was in portrait mode the whole time.