To add your own icons to Avenza Maps, you need to create a KMZ file externally with the custom icons.
One easily accessible way to do this is to use Google Earth on your computer. With Google Earth open, create a point on the map. Next, right click on the point and go to Properties. Select the pin icon in the top right, and change it to either one of the custom built-in icons, or add your own custom icon. The best format to use is .png for icons as they allow transparent backgrounds (prevents the white background around the icon).
Once your new icon is on the map, right click on it and select "Save Place as" and save it as a .kmz file. This .kmz file will contain the associated graphics necessary to import into Avenza Maps. Store the .kmz file in a location that can be accessible to your mobile device for importing (iTunes File Sharing, device storage, Dropbox)
On your mobile device, open the Avenza Maps app, and open a map that has the same extents as the feature you created (using the 'Getting Started' map is ideal for this). Once the map is open tap the Map Feature icon (next to the wrench), and select Import ('+' icon on Android devices, square with the downward arrow on iOS devices). Navigate to where the .kmz file is located and select it to import.
Once the .kmz is imported, the icon will be available in the placemark icon list when creating new placemarks.