That is a very odd situation. I would contact LinkedIn Support and ask them if there is any sort of bounce back coming to them on their end. I use my O365 email on my linkedin with no problems.
You may also want to check your block list in Office 365. You can do this by clicking on the little Gear icon on the top of the page when logged in, and type in block and it should pull up an option for Block and Allow. From there, I would check those lists and see if an @linkedin.com email is listed.