Hi,
I don't think that the latency of RTMP is relevant in a local network.
I know that VLC add some latency so you must consider to use another player (Flash, AIR, ffplay...)
About screen sharing I suppose that you use OBS. It can add few latency because it is optimized to get the best video quality rather than getting the best speed, but if you really need to get low latency you can contact the OBS team. There are also some tips on the internet (for example see
this page).
Otherwise if you are on windows it is also possible to capture the screen with ffmpeg and the gdigrab parameter :
ffmpeg -f gdigrab -framerate 15 -i desktop -pix_fmt yuv420p -movflags +faststart -g 5 -q 5 -x264-params bframes=0 -preset superfast -tune zerolatency -f flv "rtmp://127.0.0.1/tmp/video" But I don't know if it gives better results.
I hope it will help you!
Best Regards
Thomas