Much, if not most, of the blame for the demise of Flash on mobile devices has been laid at Apple's feet. The iPhone completely changed the mobile phone market in 2008 when the company launched the App Store. Smartphone platform creators had previously allowed anyone to write anything for their platforms, but not Apple. Steve Jobs believed in completely controlling the user experience and with iOS, he had an opportunity to do what couldn't be done for OS X. Every single app for the iPhone would meet a set of criteria and be officially approved by Apple.
Flash didn't meet those criteria, and so it was never allowed on the platform. In April of 2010, Jobs wrote his "Thoughts on Flash" manifesto, which in no uncertain terms said Flash would never be allowed on iOS. HTML 5 was on the horizon then and its success has put the final nail in the coffin of Flash for mobile devices.
However, long before the iPhone was released in 2007, Flash was alive and well on mobile phones. Not only was it available, it generated revenue for Macromedia. In early 2003, DoCoMo licensed Flash Lite for its iMode phones in Japan.
According to Michael Mace, Palm's former chief competition officer, when it came time to get Flash on other platforms in 2003 and 2004, Macromedia ran into a problem. Unlike DoCoMo, no one else wanted to pay. They expected the Flash viewer to be free. That was the original model--the viewer was free and the developer tools were the source of revenue. It worked great on the PC, so much so Adobe paid over $3 billion for Macromedia to get Flash.
Macromedia feared losing its revenue stream from the Japanese market so it declined to offer Flash Lite to other carriers around the world for free, at least for a few years. By the time it was free, it was too late. As Mace points out, users grew accustomed to not viewing Flash on their phones and howls of protests declined. HTML 5 came along and made Flash redundant.
Now the platform is being wound down for mobile devices. This is only the beginning too. Flash for the desktop will be the next to go.
I wonder how the mobile landscape would be look today had Macromedia chose to license the mobile player to manufactures at no cost in 2003?