Thank you Bjorn. However, I'm not sure that my question was fully answered. I have a Web Map saved within "My Contents" online at ArcGIS.com, but it's not showing up as an available Operational Layer. Am I missing something? Should it be saved as a different type?
I have the exact same issue Jason, I have created a web map with operational layers but they do not show up in my content within the flex application builder.