I have a user with a Iphone6, it will not sync all the exchange contact information with his Iphone6, some of his contact's have exchange linked and some don't. 

Hi,

Basic on your post, I want to double confirm whether all iPhone 6 device or just one experience this issue. Besides, what the meaning of some of his contact's have exchange linked and some don't?
Please post more details for further troubleshooting.
Please open OWA to check the contact information.

Heres an article about Synchronize Outlook and Apple iPhone or iPod touch contacts, for your reference:
https://support.office.com/en-us/article/Synchronize-Outlook-and-Apple-iPhone-or-iPod-touch-contacts-149cbfc5-4396-4ab3-8b65-22915e4043dc

If the issue persists, please contact Exchange Mobility and ActiveSync Team so that you can get more professional suggestion, for your convenience:
https://social.technet.microsoft.com/Forums/exchange/en-US/home?forum=exchangesvrmobilitylegacy

Thanks