Syncing non-Amazon purchased eBooks between Kindle, iPad, and iPhone
You can do this depending on the file type. Install Amazon's Send to Kindle for Mac. It's a free app that lets you send your personal documents to your Kindle devices and Kindle iOS reading apps from your Mac. 

You can send using drag and drop, or from the Finder, or from other Mac apps via the "Send to Kindle" option in the Print menu. You can also choose which devices and apps you want to send to. 

The documents you send must be one of these file types:


Microsoft Word (.DOC, .DOCX) 
PDF (.PDF)
TXT (.TXT)
RTF (.RTF)
JPEG (.JPEG, .JPG) 
GIF (.GIF) 
PNG (.PNG)
BMP (.BMP)
MOBI (.MOBI - used for eBooks)


If your file doesn't meet these requirements, you can always use a tool like Calibre to convert it to a compatible type.

When uploading .MOBI eBooks these need to be DRM free.

There's more info on using the app on Amazon's site.