A family of Microsoft products that enable users to capture, organize, and reuse notes electronically.
If you read through the previous postings, you will see that your in good company.
As for my original posting, assuming that you have a OneNote account already, you may be able to directly access OneNote on the OneDrive site https://onedrive.live.com via Fire's Silk browser. It's slower and not as "seamless" as it should be but it does work.
The other way that I mentioned (sharing) is only because some users can't seem to get to the onedrive.live.com site directly as was previously mentioned.
This method is not for everyone and not a "happy" solution but it is what it is: the ability to link the Fire to OneNote and back for the really important stuff in our lives.
I'm looking at EverNote as a replacement app.