Most MMORPGs I've played make you download giant sized files that contain the game's assets, likes images, maps, items and all that stuff. My question is, how would a Flash MMORPG do the same on the same scale? For example, my game might have thousands of images for skils and sprites and that kind of thing. I don't see too many players waiting around to load a flash client that is that big so I'm thinking that perhaps you load the content as the user comes across it (as opposed to all at once). I'm just looking for any insight on how this is achieved.

This isn't specific to Flash. Many MMORPG's do it already. For instance WoW features a "live client" which initially downloads what you absolutely need (core content and the actual software) and then streams the rest (assets) as you play, saving it on the hard drive so that it's only downloaded once. On the other hand, if you can't save the content on the hard drive (e.g. Flash without user permissions) then this is going to suck in terms of bandwidth usage (since players would most likely be downloading exactly the same thing every time they fire up the game). And browsers may not be happy dealing with gigabyte-sized caches so you may need to configure Flash so that it dumps its stuff elsewhere (I know I regularly flush my browser cache).

That said, if you haven't started developing the MMORPG yet then technical details like those are the last thing you should be worrying about at this time. You should not worry about "getting it right" because otherwise you'll never get started. Just prototype, iterate, don't worry about bad code or hacks - you will naturally go back on them as you learn good code design from failing repeatedly - and then you'll succeed (hopefully)