I have managed to get mine working. It's a security problem with chrome not allowing the scripts to be loaded.
Solution:
1. Open the extension folder
For linux users (Ubuntu) : ~/.config/google-chrome/Default/Extensions/
For Windows users (Seven) : C:\Users\[username]\AppData\Local\Google\Chrome\User Data\Default\Extensions\
For Windows users (XP) : C:\Documents and Settings\[username]\Local Settings\Application Data\Google\Chrome\User Data\Default\Extensions\
2. open the folder for AMR
For me it's "nhjloagockgobfpopemejpgjjechcpfd"
3. there should be a folder with AMR version number. Open it.
4. Open "manifest.json" with a text editor
5. replace this row:
"content_security_policy": "script-src 'self'
https://ssl.google-analytics.com https://community.allmangasreader.com/ https://www.google.com/ https://platform.twitter.com/ https://www.facebook.com/ https://raw.github.com/ ; object-src 'self'",
with this:
"content_security_policy": "script-src 'self'
https://ssl.google-analytics.com https://ssl10.ovh.net/ https://community.allmangasreader.com/ https://www.google.com/ https://platform.twitter.com/ https://www.facebook.com/ https://raw.github.com/ ; object-src 'self'",
6. Save the file
7. Open extensions in chrome "chrome://extensions/"
8. Under the AMR extension should be a link that says somehting like "Reload (Ctrl +R)" Press it and AMR shoudl start updating again. (I dont know the wording on that link since mine is translated to swedish)
The thing we add to the manifest is "https://ssl10.ovh.net/". This is the repository for all the scripts that reads the dirrerent manga sites. Chrome dident like to read it without it being in the security options.
Hope this helps!