Flash templates and web templates are actually the same thing and the difference is that flash template is a design developed in flash (partially or completely).
The good thing about flash templates is that flash technology allows creating really impressive things so your product represented via flashy web site will get more loyalty and is likely to be purchased.

Not very comfortable thing about flash templates is that they require some knowledge of flash to add your info into. Of course, you can always hire a freelancer (there are lots of them) to do all the work for you… 

People like Flash for many reasons but you should keep in mind that to use or not to use Flash (thus flash templates) depends mainly on your site’s mission. With some sites – mainly content orientated it’s better to avoid this technology as with such site people want the information to be loaded in a fast manner.

But if you want to add dynamic to your site to show all the benefits of your products or services flash template is the right way. But make it sure that your visitors will enter flash site otherwise they can just left it without seeing all of your promotional materials.