You can stream video for free if you're an Amazon Prime member.
Every once in a while, Amazon will offer credits for Amazon Video as a purchase incentive for certain products. But those credits usually are not enough to get a video for free and expire quickly.
There might be illegal websites where you can download video files to your Kindle but you run the risk of also downloading a virus or malware. You would need to find files formatted for the Kindle, which could be tricky.
You'll also have to take the storage capacity of your Kindle into consideration. Most full-length feature movies take up about 1GB of space. My Kindle Fire has a 16GB capacity, which has to hold the operating software, my books and apps. I don't know how many movies you would be able to store without affecting the ability to also use those features.
You can't download movies to any device for free unless you have purchased a dvd that comes with the digital content that you are allowed to rip onto other devices. If you ever find a place that lets you download movies for free come back and let us all know.
You can watch movies on a Kindle fire if you have Amazon Prime ot Netflix subscriptions but you have to be near wi-fi to watch them unless you have the big new fire that has 4g.