To save bandwidth, most of servers will practice some hotlink protection, usually using either following script to check whether the HTTP referer is come from the same server, most script are focus on image file, but it can slightly modified for FLV protection. There are two common methods to do that:

Edit in .htaccess RewriteCond %{HTTP_REFERER} !^$
RewriteCond %{HTTP_REFERER} !^http(s)?://(www\.)?yourdomain.com [NC]
RewriteRule \.(flv|mp3)$ - [NC,F,L]

Edit in httpd.conf, first enabled this:
LoadModule setenvif_module modules/mod_setenvif.so
then put it inside <VirtualHost>, just before </VirtualHost>
SetEnvIfNoCase Referer "^http(s)?://(www\.)?yourdomain.com(/|$)" local_ref=1
SetEnvIfNoCase Referer "^$" local_ref=1
<FilesMatch "\.(flv|mp3)">
Order Allow,Deny
Allow from env=local_ref
</FilesMatch>

However, FLV need to play through Flash Player, different browsers and even minor versions handle plugin HTTP referer differently, so it make such hotlink protection through HTTP referer means impossible :(

Browser sends the URL of the requesting plug-in (i.e. the best situation, url of SWF) does not send a referer sends the embedding page URL
IE X    
Firefox   X  
Safari (MAC)     X
Safari (Win)   X  
<Chrome 3     X
Chrome 3+ X    
<=Opera 9     X
Opera 10+ X    



The hotlink protection cause problem when you let other people embed your video player in their site (like Youtube do), from the above table, you can find the third column will not work, for example in safari (MAC), the video cannot play because Apache think the FLV is linked by third party website and forbid FLV to be accessed.