Hi DinakarGeddapu!
Have you clicked on the "play live chess" option in the Facebook app?
If both you and your friend have chess.com accountd and are both online and in the live chess arena at the same time, you will be able to see each other in the "friends" tab and play!
How do I play live chess with facebook friends where the players can see the moves real time? The facebook app either allows to play with a random person realtime or with a friend where I have to constantly refresh the page.