There is no source code for a figure that you can view (the figure creation code was probably originally written in C, C++, Java or similar language, and other than working for Mathworks you won't have access to it).
There is a tool that can generate m code to recreate a particular figure, but I don't think that's what you're after.
It sounds like you want to create a GUI with your own figure menu. If so, look at the documentation here and in particular, Create menu for GUIDE Apps if you intend to use GUIDE to create your GUI or Create menu for programmatic Apps if you intend to use App Designer. If you're familiar with neither, I strongly recommend you use App Designer as you'll have less of a learning curve.