Is this situation likely to change soon? Or is there some deep reason for it, which is likely to make it last a long time?
IMHO, Amazon most likely hasn't updated the Kindle for Windows and OSX apps, because not enough readers demanded custom dictionary support. (BTW, Amazon-bought dictionaries can be sent to the Kindle for Android app.)
Until Amazon fixes ...
New (April 2014) Solution:
Go to Amazon Cloud Drive (https://www.amazon.com/clouddrive/).
Select documents (one-at-a-time only) and click Download.
Old Solution that can work without Internet Access:
Deliver the documents/books to your iPhone or iPad Kindle.
Download & install an app such as iFunBox Classic (free). This app allows you to ...