There are two varieties of ePub: Reflowable text ePubs and Fixed Layout ePubs.
It's best to use the latest version of InDesign (CC2015) to create ePubs. You can also use plugins, to help with FXL ePubs.
To use these format on the Amazon Store they will need to be converted to from ePub to Mobi. You can do this by using the Kindle Previewer or uploading to the Kindle store and letting Amazon do the conversion.
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InDesign is a great tool for creating Fixed-Layout EPUB files. Amazon does not accept EPUB so you need to convert the EPUB to .mobi or KF8. You can do this with Kindle Previewer or KindleGen. Check out the Kindle Publishing guidelines here https://kindlegen.s3.amazonaws.com/AmazonKindlePublishingGuidelines.pdf. The key is to make sure that your FXL EPUB validates and is EPUB 3.0. I personally have not done this conversion so I have limited experience with the process. Maybe some others can provide more details.
Useful plug-ins for InDesign worth looking at is CircularFLO Home - CircularFLO
As Chad mentioned (I thought you were on your hols Chad!) you need to validate your ePub – have a look at this: EPUB Validator (beta)