Microsoft introduced outlook.com to the masses. It is cleaner and simpler. If you upgraded to outlook.com email address or using it as an alias, most smartphones or tablets don’t give option for setting up outlook.com as email account. You can set up outlook.com email address account on your Kindle Fire Hd or Kindle Fire 2 easily.
Just use Hotmail option when setting up email account for any Microsoft email address like Outlook.com or Hotmail or Windows Live ID email accounts. That should be it. You can find below detailed steps if you need them.
How to setup Outlook.com/Hotmail/Windows Live email account on Kindle Fire HD/2
1. Go to Kindle Fire HD/2 settings by swiping down from top of the Kindle Fire HD screen & tapping More
2. Tap on My Account > Manage Email Accounts
3. Tap Add account & select Hotmail

4. Enter your outlook.com email address, password

5. Thats it. Your outlook.com or windows live id email account should be setup. Your email should start to download. Kindle Fire HD keeps your email for 3 days only on your device. You may want to change these settings by going to Menu > Settings > Store messages Forever.
If you need Incoming or Outgoing Server settings for Outlook.com, You can find them below. Exchange Server address is blu-m.hotmail.com & It uses SSL. These might be useful if you are setting up email accounts manually etc.

Also read, how to airplay from your Kindle Fire HD to TV