Hi George
It sounds like you may be having a problem caused by fonts substitution. Are your fonts OpenType or TrueType? Postscript Type 1 fonts are not supported in EPUB.
I’d need a bit more info though before I can help further… When you say ‘It works fine online via a browser’ how are you viewing it? Are you viewing the EPUB or the individual pages in a browser. If so, you may have the same fonts active on your computer for use in InDesign and therefore they are working in YOUR browser, but they are not the fonts from inside the EPUB.
When you say ‘when take it into iTunes Producer’ but have you first viewed in iBooks on the Mac, what do you see there?
You mention Amazon in the title of this post, but it is not easy to get to Amazon from an InDesign generated fixed layout EPUB. My company’s software CircularFLO https://www.circularflo.com may be able to help you there…
I’ll try to help you if I can have more info.
Ken Jones
Circular Software