[j_cool]

This one works fine:

set url=http://www.filmon.com/channel/bbc-news
start /min streamlink --http-header "User-Agent=Mozilla/5.0" --player "ffplay.exe -vf scale=854:480" %url% worst


This one not so fine:

set url=http://www.filmon.com/channel/bbc-news
start /min streamlink --http-header "User-Agent=Mozilla/5.0" --player "ffplay.exe" %url% best


You can dump the stream on disk, wait for some stream to get saved on disk, and play the stream from disk with any player.
Mplayer, FFplay ...

This way there are no tea breaks, but one second more or less between chunks.

Python guys know how to sort it out or somebody like rtmpdump team.
Look at Vaughnlive.py, one example of excellence of stramlink/livestreamer team.