Video playback in the browsers on most smart phones is a work in progress. I have the Motorola Droid and its online video playback is also relegated to a youtube app. I have tried several browsers like Dolphin and Opera mini but none of them support video playback And, while I suspect that adobe is working on making a flash plugin, if it is anything like the time frame for the acrobat reader (just released it a month ago) we won't see it for another year.
I would say go with flash, all the major TV networks use flash, Netflicks is using flash, and all of Hulu competitors are also using flash. So I would say the trend leans heavily towards flash. And then for smart phones make some apps for the time being until they get up to speed.
And then there's HTML5 which can play video but browser support looks pretty grim.
Yikes that's a mess. Looks like someone is going to have to start and open source community for developing a standard open source web codecs for HTML5. Something like what was done with php, w3c, mozilla, open office and others.
