The possible way out:

1.Go to web, menu, settings. Then scroll down until you see enable flash.  

2.Try your luck to use the Kindle Fire Silk browse play flash.

3.I switched to desktop rather than mobile view.

Is there any definitely workable solution? Yes. Doremisoft Flash to Kindle Fire Converter for Mac can be your great helper, which can convert Flash movies like FLV or F4V to MP4 for Kindle Fire without quality loss. After the conversion is done, you need to transfer the generated file to the Kindle Fire. Finally enjoy movies on Kindle Fire. Though it seems to be a bit troublesome, it enables you to solve the problem thoroughly.  

More advanced features with Mac Video Converter for Kindle Fire:

1. The program offers more presets for popular devices except Kindle Fire:

iPad, iPhone, Samsung Galaxy Tablet, BlackBerry smartphones or Tablet, mobile phone and so forth

2.Enables to edit almost any video in popular and professional Mac editor:

You just need to convert the source file to the editing program supported file format, by selecting the editor name. 

3.Do some easy and practical video editing in the program:

Video trimming, video cropping, audio extracting, video resolution settings (480x368, 720x480, 1280x720, etc) and more.

OS supported:10.7 Lion, 10.6 Snow Leopard and Mac OS X 10.5 Leopard 

Guide on how to play Flash with Kindle Fire on Mac:

For preparation: download and install the Mac Kindle Fire Video Converter on your Mac.

Step 1: Add flash video from your PC Hard Drive to Converter by clicking "Add File". 

Step 2: Choose "Kindle Fire" under the output selection. 

Step 3: Hit "START" to start converting Flash file to MP4 for Kindle Fire. 

Step 4: Connect Kindle Fire to your Mac, transfer the generated .mp4 to Kindle Fire and watch movies with ease.