I've set up a local RTMP server as well. What I've found is you can't directly use the RTMP as a video. You'll probably have to set up a video player locally as well, such as flowplayer or something, on a local web server, and make it so whatever you are sending over the RTMP, the player picks up. Then, use the URL the player is on for the video in one of the theaters. Also, you can choose to install the player and RTMP server on a VPS or something similar if you have one.

I will not outright say this will work, as I'm still getting it set up to test on my end, but it seems more likely to work than anything else.