Yes, u definitely can. Just use keepvid.com to download youtube vids. When you access Youtube videos then they get saved in cache folder in FF and Temporary Int Files folder in IE. Just copy those file by arranging in ascending order file size and run it using FLV Player.
I often use the moyea flv play to play flv. But i am not very clear about how to make a custom player. If easy, who can provide the codes. I would like to make a own one.