Make sure you used the right codec settings for the mp4 and the right codec for the .flv (which is a container). Flowplayer requires pretty default encoding settings. Please refer to the Flowplayer site itself for info about that.

I just tested a few video's from your site with the official 1.4 release and with the latest nightly.
They work fine !
I guess there must be something wrong with your installation but I can't suggest anything apart from a complete reinstall.

The flowplayer plugin is working now! I started very simple with the simple install from the flowplayer site. When I installed the files on my server it's wasn't working either and I had the same black box. With the help of the flowplayer forum I found out that gzip for swf files had to be disabled on the server. So I installed 2 .htaccess files:

file 1 in the same folder as the .swf files (/zenphot/zp-core/zp-extensions/flowplayer3):
Options +FollowSymLinks
RewriteEngine on
RewriteRule . - [E=no-gzip:1]

file 2 in the album folder (/zenphoto/albums):
SetOutputFilter DEFLATE
SetEnvIfNoCase Request_URI .avi$ no-gzip dont-vary
SetEnvIfNoCase Request_URI .mov$ no-gzip dont-vary
SetEnvIfNoCase Request_URI .mp3$ no-gzip dont-vary
SetEnvIfNoCase Request_URI .mp4$ no-gzip dont-vary
SetEnvIfNoCase Request_URI .flv$ no-gzip dont-vary

The first file disables gzipping for swf-files. After this the flash-files are working, but in my case mp3 and mp4 isn't. So i decided to disable gzipping also for all audio and video formats in the folder (and subfolders of) albums. After this all the file formats are working.