When I check the internet speed statistics through speedtest.net it shows properly on the laptop. But when I do the same thing for my mobile phone it doesn't work well. In fact, it doesn't work at all. My mobile phone is capable of running flash games and access other sites like Neeraj Kulkarni blog and Yahoo which do require flash player to run properly. What is the reason? Please help.
Flash Player is not supported on mobile devices (Android, Blackberry, iOS, Windows Phone). See Adobe Flash Player | Tech specs for supported operating systems and browsers.
If speedtest.net requires Flash Player then it's not going to work. It's possible the other sites you mention have implemented solutions for Flash Player on mobile.