It appears to be a problem with the project. I have another project in the same workspace that has the iOS option enabled. I could recreate the project, but hopefully there is an easier solution.
I just created a project with Adobe Launchpad (http://labs.adobe.com/technologies/airlaunchpad/), and it looked like I setup all the options for iOS, but when I go to run configurations and try and deploy to an iOS device I'm getting the same problem: "This platform is not currently supported for Flex Mobile projects"
Anyone know why?
I just discovered that when I try to create a new mobile project in Flash Builder the iOS checkbox is missing in the wizard. I was however able to copy a project with iOS support and the new copied project does have iOS support. I used Adobe Launch Pad to create the original project so it may be causing the problem.