Short answer. No. Sorry for the rest of this, but you touched a subject that constantly aggravates me.
I have used it successfully on FreeBSD-9.x. I haven't tried with 10. I do know it requires HAL, and I have been using X without HAL on FreeBSD-10.x. (The new x11-servers/xorg-server doesn't require HAL to run.)
VERY LONG DIGRESSION:
For what it's worth there's a thread that is up to 201 posts about Amazon Video not working on Ubuntu. In a nutshell -- it worked with Linux, then upgrades to Linux (or possibly Flash, I've forgotten by now) led to it no longer using HAL. At that point, it stopped working. There are various solutions that sometimes work, such as installing a special HAL package (and in Fedora fake HAL, if I remember correctly). However, Amazon first said: "Sorry, we're working to fix this." They then did fix it, and the next updates worked. However, then they broke it again, and this time, their official stance was, sorry, we don't support Linux. This means that even if you get it to work (on Linux or a BSD), it doesn't mean that it won't break in a week, and Amazon doesn't care.
The only thing one can do is vote with your feet. If you use their Prime for shipping, well, you do, but if you were planning to get Prime for the instant video, it may be worth writing and telling them why you aren't. If enough people write, they may at least start to support Linux.
The same holds true, at least for me, with YouTube rental videos. It will play for me on Linux, but not FreeBSD, so I wrote and asked for a refund, saying that I paid for a rental and I should be able to watch it on whatever workstation I have.
The irony here is that the only ones who get hurt by these things are those who are looking to purchase things legitimately. I've heard it said (Slashdot article? I don't remember) that there are three broad categories as far as media and pirating. Those that will pirate, no matter what. Those that will never pirate, no matter what. And, what may be the majority, those who will pay if it's convenient enough, but if it becomes too much of a nuisance, will pirate. The various protections offered by Amazon, or YouTube rental -- things that are apparently not that necessary, as Hulu works at least for me, on any OS with a browser that has Flash, so, while I'm too old and stodgy to pirate, I'm sure all these protections -- that the people who would pay wouldn't need -- do nothing but cost them customers.
Apologies for the rant, but literally, within the last hour, I rented a YouTube video that wouldn't play on FreeBSD. Maybe if everyone who used FreeBSD rented a movie and then asked for a refund, they might start worrying about it.