to run fixed you will need add a cog and lock ring to the other side of you hub. If you keep the same or similar tooth count o the new cog as your freewheel, you will not need a new chain. it looks like you have a 17 tooth (17T) freewheel based on your link.
Best play to pick them up is a your local bike shop unless you want to buy the tools to install them.
for example:
cog:
All-City standard track cogs | Retrogression
Lockring:
'Steel Reserve' stainless steel lockring | Retrogression