Yeah. Resizing of images usually ends up with pixellisation. Sadly there are no algorithms I know of that do it perfectly... (Yet).
I don't quite understand what you mean by "go to Http://Etc.Etc and go to a place in the code that's always in the same place (that is a image URL) and post it somewhere that flash could read it... " - you mean, like, importing text into flash? You can do that with PHP, or simple txt files. Adding images is harder, but I think I have an example somewhere on my HDD of it... *Goes off to look for them*
EDIT: If you've got Flash 8 Pro (I don't know about others) there should be a folder called "Samples and Tutorials" in the flash install folder... In that, samples\ActionScript\LoadText covers importing HTML files into flash... Although I'm not totally sure if it works perfectly. All you need to do then is code a PHP file to generate the HTML code... and yes, there are scripts which display images from a database if that was what your question was.. I can't say much. I can only code PHP when I have cheatsheets out (Actually, that's a lie; I can only code database parts of PHP if I have a cheatsheet.. The others I can either guess or just do... However, much simpler to use VB/C#/whatever + ASP.NET...