If you want an installable desktop app of your mobile project in Flash Builder you can:
- Click on Project > Export Release Build.
- Fill in your destination directory in the "Export to folder" input.
- Change the "Export as" option to "Signed AIR package for installation on the desktop" and click the Next button.
- You'll need to have or create a new digital signature. Click the Create button and fill out the form to have Flash Builder create it for you.
- Then hit Finish and it'll build an AIR app that you can install on the desktop OS.
I'd suggest setting some values in your APPNAME-app.xml file in your project. I set resizable to false, width to 640 and height to 960 so that it would mimic a mobile iPhone 4 app. I also made sure my application identifier (id) was set, along with filename, versionNumber and versionLabel.
If you'd like to put your app on your website, Michaël Chaize has a great post on how to run a version of your Flex app in the browser. Basically you create a new non-mobile project, add the mobile components, override some classes for states and orientation changes you'd have on a device, and include the mobile skin and you're finished. I have not tried this yet, and I don't know if there are any caveats or restrictions with this route.