Hello Scott,
I do not believe that map axes can be used with uifigures (which is the type of figure used in App Designer). A map axes is simply a regular axes with extra metadata, and only uiaxes are usable with uifigures. As a result of this, plotm cannot be used, since it requires a map axes to function.
You won't have the same projection options, but you can simply plot latitude and longitude as y and x values on a uiaxes. Alternatively, you can open up a separate figure from within your app to display the map information.
-Cam
