Inside and outside should flash for both turn signals and hazzards.
https://www.youtube.com/watch?v=3ZlwKPycDYc
Based on what's happening it sounds like you've got something crossed and as a result the resistance on one of the flasher cans is different, causing it to blink rapidly. First thing to check is simply to see if a bulb is burned out.
Another thing to look at is the sockets themselves. Mine were pretty severely corroded and needed replacing.