Yes, I was able to get this to work with the 1964 imagery as well:
http://arcg.is/1QGDAet
Steps:
1. Opened a new web map
2. Set the basemap to World Imagery, saved, and shared with Everyone
3. Opened a new web map and added the 1964 imagery by going to Add > Search for Layers > Specified the ArcGIS Server URL
4. Saved the web map, shared with Everyone, and then created the web application. This time I chose to use two web maps
Note: all of the above steps were performed in Firefox
Does the above application work for you in Chrome?