The best technology to use is probably the one you're most familiar with, unless you mean you're going to be learning on the fly. But for the various options I'll take a stab.
Flash itself (the runtime) is a browser plugin, so that's not what you want, but if you build your application in Flash or Flex (the authoring tools), then you can publish it as an AIR application. AIR is also a runtime - basically it's Flash, plus a bunch of extra APIs for running outside the browser. The advantages to making an AIR app are:
- The same app runs on win/mac/linux
- You can make it with the same skills/tools you use for Flash (dubious utility if you don't have those skills/tools, of course)
- Close tool integration with other Adobe tools (photoshop, after effects, etc.)
The main disadvantage is incomplete access to native (i.e. OS) capabilities. The way a runtime allows you to run the same app on win/mac/linux is by restricting you from doing some of the things that you could do with a native application.
As for Flex, whether you use Flex or not is a separate question. Flex is a framework within Flash - an AIR app can be made using Flex or not using it. Basically, if you expect your app to have a lot of controls, slider bars, charts, accordion panels, etc., you might look into Flex. If you expect it to have a lot of animations and pictures and sounds, plain-old-Flash may be better.
Apart from Flash, the other main choice for a runtime is Silverlight. The advantages there are, to be honest, basically the same. You use .NET instead of ActionScript, and the tooling integration is with MS' Expression suite instead of Adobe's creative suite, but the development process and the results are quite similar. The choice between AIR and Silverlight is really a choice between Adobe tools and MS tools, and between two programming languages of entirely comparable power. Most everyone simply uses the one they're more familiar with.
Finally, the other set of options is not to use a runtime, and to simply compile an app from any language/development environment you like - C, C++, .NET, Python, anything. The advantage here is you get (in general) full access to OS capabilities. The disadvantages are, you (in general) need to do extra development to run on multiple platforms, and also I don't think you'll find a language/environment that lets you work with multimedia as easily as you can in AIR and Silverlight.