Kirti,
JFBConnect uses Joomla standards to create Joomla users and can be integrated with most other extensions. We don't have specific support for Flexicontent, but you can easily add Like buttons, comment boxes, or other widgets to any other component output. Users can login using Facebook and will be seen by Flexicontent as standard Joomla users.
In short, you shouldn't have any issues when using both together. If there was something specific you were looking to know about though, please let us know.
Thanks,
Alex