Hi, as you can see from my profile, I have a lot of experience with Chrome Extensions, so I can help you.
Unfortunately, Google doesn't provide an API for getting rank, so our extension would need to work this way:
1. You right click on any link
2. Google search for that domain and keyword automatically commences in new tab, extension gets the rank, closes that tab and presents it to you on the page the link is present.
Feel free to contact me if you have any questions or doubts.
Best regards,
Stefan