YES! You can publish your book directly to Kindle and it doesn't cost a thing! Everything you need to know is on their homepage:
Kindle Direct Publishing
If you have an account with Amazon already, creating your own KDP account is EASY as pie.
Here are a couple of ebooks that can guide you through the process as well:
Publish on Amazon Kindle with Kindle Direct Publishing (free)
This book walks a person through the process of publishing to Kindle with easy to follow instructions
How to Publish Anything on Amazon's Kindle ($2.99)
A few highlights:
You do NOT have to have your own ISBN in order to publish on Kindle - they will provide you one. You can purchase and provide an ISBN if you prefer, but it is not necessary.
You will need to provide your own cover art. Their publishing platform provides you with the minimum and maximum requirements.
You will need to provide a Product Description (think backcover/inside flap blurb)
You will need to set a price. The lowest you can set is .99 cents. .99 cents - 2.98 give you a 35% royalty rate. $2.99 and up gives you 70% royalty.