The rtmpdump tool can help you save video streams as local files.

It comes with most Linux distributions, e.g. on Ubuntu or Debian (with sudo):
sudo apt-get install rtmpdump

On Windows, the most convenient way is probably via Cygwin and Cygwin Ports:

1. Install Cygwin
2. Install Cygwin Ports
3. On the package selection screen, select “rtmpdump”

Read the manual page and study the options:
man rtmpdump