Please check whether your device is listed in this supported list document: http://www.adobe.com/devnet-apps/flashruntimes/certified-devices.html.
Otherwise you need to check with the Sony Customer Support for this.
Thanks, Prabha. I did contact Sony, and their responses are, let´s say slippery. I would like to know if there is technical problem or a licensing problem. As it is the owner of a Sony "smart" TV is deprived of access to some od the most common internet sites, such as youtube. I also noticed no TV in the list you provided to me.
if it isn't a supported device, then Adobe doesn't have code for that machine. Check Sony forums for that TV and maybe somebody has a workaround.