iPhone 6 - Exchange calendar not showing up in list of calendars
I had the exact same problem on my iPhone 6s. I tried to delete the Exchange account and add it back again, yet the Exchange calendar would not show up in the calendars list. 

What finally helped in my case was quitting the Calendar app (not sure if that mattered), then going to Settings > Mail > Exchange and turning the "Calendars" sync setting off and then on again. 

When turning off, you get a question whether to delete all Exchange calendar data. I accepted, and then turned the sync back on. When I started the Calendar app, the Exchange calendar finally showed up.

Make sure you backup your data before fiddling with the settings and removing calendars.