phpTumb (phpthumb.sourceforge.net) is a powerfull class used in FLEXIcontent for image processing. For performance purposes, we chose to use it external of the Joomla! framework (it avoids to load the entire framework each time you generates thumbnails).
-- You do not need to set the permissions of the folder, unless you have wrong ownership of your folders (ask you provider to fix wrong ownership if you cannot do it yourself or try deleting the folder so that it gets recreated)
-- FLEXIcontent will set folder permissions to be: 755 (Read-Write-Execute) and files to 644
(NOTICE the no execute permission for files, also FLEXIcontent places an .htaccess file with deny execute directive in this top level folder)
-- if you enable joomla FTP layer (avoid it is Slow), then you will have problem with above permissions if the FTP user is different than the user than owns the files, so make sure the FTP user is the same as the owner of the Joomla folder files, or contact you Host provider to fix
NOTE: After verifying that:
-1- your (apache) web server is using suexec mode (OR A similar technique)
-2- Then check that:
a. your Joomla/FLEXIcontent PHP files
b. the phpTHumb cache folder
have THE SAME OWNER
Reference: (google it for more)
http://en.wikipedia.org/wiki/SuEXEC