Hello I Am using ffmpeg and ffserver to stream mpegts with h264 encoding on an Ubuntu Server
How Can I create a backup/alternative server so that if server1 stopped for any reason server2 takes its place?
Most services don't have such a feature build in because failover should be managed by the server itself, not by each individual service. The services Heartbeat and Pacemaker are a pretty good solution and available for every mainstream distribution.
If you need help configuring it, just Google; there are a lot of usefull resources besides the two links I provided above, such as this one.
Warning: Failover clustering will add complexity and thus more headaches to your life...