You can add a "no-store" condition to prevent FlexiCache from caching a page based on a number of rules. How this works is explained in the documentation which comes with the plugin: http://your.website.com/wp-admin/options-general.php?page=flexicache§ion=documentation#flexicache-doc-configuration (change your.website.com to your WordPress hostname)
To prevent FlexiCache from caching the homepage, create a new no-store rule as follows:
Match Type: Equals
This will prevent FlexiCache from caching anything where REQUEST_URI="/", which is the URI of the home page.
Once you have done this, FlexiCache will no longer cache that page. Bear in mind that if the page has already been cached, it will continue to be served up until the cached item expires, so you may also want to clear the cache to see this configuration working immediately.
Hope that helps!