Is there a html5 video player for Drupal 6 that run well on ios device? I need to play videos on my drupal 6 site that would run well on IOS device (HTML5?).
Is such solution available?

My site currently serving flv files using jwplayer 6.x-1.1.
Yes; try jPlayer: http://drupal.org/project/jplayer

Note that you might be better off implementing this directly (as I did recently) than using the module since the module supports the older version. You will also need m4v files to play video on iOS devices.

I implemented it by following their Quick Start Guide and placing the HTML and JS into my theme, tailored of course to be Drupal-friendly (i.e. using Drupal.behaviors for the JS and using preprocess functions to set file paths properly).

It works well, and my iOS-using client was able to listen to audio (I implemented it for audio) from their iOS device without issues.