I have a flip flop hub currently with a fixed on one side and free cog on the other. I wanted to know if it's possible to make both sides fixed or both sides free. Or is each side exclusive to a particular type?

You can do both but neither is correct. There are fixed/fixed flip-flop hubs which is what you really want.

You can put a free wheel on either side (which makes fixed/fixed better than fixed/free). In order to put a fixed cog on the free side, you'd have to do what people with conversions do and use a bb lockring.

Otherwise known as a suicide setup.

If you want the widest possible use out of a hub, then fixed/fixed is the way to go. You can put a freewheel on the fixed side no problems. Doesn't really work the other way around.