Looking at the logs, there are various explanations for this issue. My was a little more stranger than usual: Flickr would say failed, while WordPress would correctly show the test post.
I found my solution looking at the logs.
[client xxxxxxxx] PHP Fatal error: Allowed memory size of ********* bytes exhausted (tried to allocate ***** bytes) in ****************/wp-includes/cache.php on line **
See also: http://www.ktulu.it/2008/01/12/fatal-error-in-wordpress/
The solution was simple; just add this line to your .htaccess file (assuming your can access it)
php_value memory_limit XX000000
where XX you can put your reasonable amount of memory (those are bytes).
Maybe you can tweak it raising it step by step. Simply writing down a large amount is not very healthy.
Anyway, 99% it’s your side fault, not Flickr fault.