Calendar syncing with Outlook is possible, though somewhat kluge to set up. Once set up though it will automatically sync. Here is how I did it on my Android devices.
- Set up a Google Calendar via the internet. (You can do this via your PC.)
- Install and set up Google Calendar Sync on your PC. (This allows Outlook on your PC to sync with your Google Calendar.)
- Install an app like CalenGoo on the Kindle Fire and set it up to sync with your Google Calendar. (The calendar app you install must be able to sync with Google Calendars.)
Basically you are syncing your Outlook calendar to your Google Calendar then syncing your Google Calendar to CalenGoo on the Fire. As i said it is kluge but it works automatically after you get it all set up.
I've not found a way to sync Outlook contacts to the Fire. However, you can import your Outlook contacts to your GMail account then import those into your Fire. Again, it is kluge and it requires manually updating the list on both the Outlook PC and on the Fire.
The only way to sync calendars and contacts directly with Outlook would require rooting your Fire then installing Google Services. Even then there is no good way to sync the contacts that I know of.