I haven't seen it but probably not, the regular htc one has a custom built flash, that is maintained by htc. Adobe dropped support for mobile devices a little over a year ago. And besides Google hates flash (chrome for android has never supported it), they are trying to push for higher html5 adoption.
If you really wanted it on the ge, all you would need to do is download it from adobe's website and sideload it.
Sprint GS3 Running TN's Msg and Chubbs