is it okay to date an ex's best friend

Not good form. Not as bad as your ex's sister or brother though.

I few weeks ago I ended my 'flirtationship' with this guy, we never really got passed the talking stage. During this time he introduced me to his best mate who I got on with. Fast forward to today I've been messaging his best mate quite a lot and we've both admitted we like each other however the first guy doesn't know we've been getting closer. I personally don't feel like it's my responsibility to let him know and personally would feel very awkward having the 'I now like your best mate' talk with him. Any advice?

There are 3.7 billion guys in this world, you will find someone you like without the drama.