This has recently been discussed on the Google Earth Help forum.
Apparently this is a bug or a current limitation of Google Earth on iOS platforms. Only workaround at present is to have the KML/KMZ refer to inline images with full URL located on a public web site.
Doesn't matter if embedded image is PNG or JPEG or uses STORED or DEFLATE compression. Google Earth does not currently display the inline images in balloon popups if images are embedded in KMZ on iOS platform.
This greatly limits the usefullness of the KMZ files but it's only a temporary condition. It has been reported to Google and hopefuly soon an update to GE will fix this.