Forget about FLV's already. It's a DEAD format. Use MP4 only and your videos will be playable anywhere: PC's, tablets, smartphones, smart TV's etc...
Just make sure you are using an appropriate player that supports both Adobe Flash (for PC's if available) and HTML5 for other devices. Check this out:
http://wordpress.org/plugins/kvs-flv-player/ - it works with both Flash and HTML5 and it's
absolutely free even for commercial use 
