No unfortunately the Fire Stick isn't a supported device, no app and watching in a browser won't work.
Have a look at the following list of supported devices as you might find you already have something that you can watch entertainment on. If not, a NOW TV box is probably your cheapest option.
If you do have another compatible device such as a games console, Roku, Chromecast etc that you want to set up, you can find more details here
Given Comcast have recently allowed Amazon on their devices and vice versa in the States, I am hopeful this will happen some time in the future with Now TV.
I don't own a Now TV/Roku stick, have had in the past, but I have moved over to the Amazon Fire Stick which I personally prefer over NowTV/Roku.
Ideally having Now TV on Amazon Fire TV and Amazon Prime on Now TV is what should be pushed for.
I have tried side-loading the firestick app by using the downloader. There are several tecchy sites that claim you can run the Now TV app on firestick and provide download URLs. I have tried three different URLs. The Now TV set-up file will download and you can install the app. However, when you launch it it hangs for a few seconds and then just kicks you out. It does look as if it has been blocked from running (and I have checked the right boxes in settings to enable unknown apps). If anyone has cracked it I would love to know,
You know, if someone ever gets the Now TV app to run on an Amazon Fire Stick Now TV will issue an update that will kill or auto delete their app. You see, Now TV's unsung policy is to zap or not work with any "feature" they do not explicitly support.
That's just the way these guys roll.