I wanted to make a website that would let users record a small video message through their broswer and save it to my website.
As I have never used flash, i wanted to know what softwares would be required and what programming languages would I need? I mean, what should I go about learning to implement such a site. I would prefer open-source solutions wherever possible.
Can something like this be implemented using python and html5?
There are many video solutions.  Here are two:
Take a look at Flash Media Server (FMS).  You will need to some server-side code to place the video into a folder as it streams up.  
Also, if you're looking into free open-source take a look at Red5.
Flash video record on website tutorial