I've had quite a bit of experience with Sony bravia although this isn't a solution to your problem with flash there are some work around i can think of.
one option would be to use long HDMI cable they can be purchased from amazon inexpensively., but most people don't want a cable dragging through their house and i don't blame them.
another option would be wireless HDMI this is the same a a HDMI cable but it uses Wi-Fi rather than a cable they can be quite expensive. if you are watching TV you need to pay attention to the resolution the Wi-Fi HDMI supports and make sure it supports a resolution you can tolerate. generally the higher then HDMI cable resolution supported the higher the price, i would go for a middle of the range resolution 1080x900 being one of the best 800x400 being the lowest (approximate resolution values)
another option would be to record the show its not an ideal solution i know but it may be suitable for your needs
http://www.ehow.com/how_8500113_record-live-feed-off-internet.html
this link describes recording live broad casts
http://www.ehow.com/how_7314996_record-tv-shows-internet.html
this link describes recording tv show with a schedule.
a problem with Sony is getting a picture or video in a format that can be streamed it can be quite fussy there are several solutions
https://community.sony.co.uk/t5/televisions/how-to-play-mpg-files-on-sony-bravia-solution/td-p/19167...
this is a codec for TV streaming that goes in the folder of the files you want to stream and puts them in a format the TV understands.
i personally use Nero media home for home streaming it will decode almost any file to the tv without fussing with media files.
another option is to use an internet link device such as steam link, NVidia shield or by building one, micro itx mainboards are around 100-200quid and no bigger than your hand they include built in graphics a built in processor and no need to worry about heating as they don't need any, slap it in a tiny itx box and it will turn you bravia into a pc. you don't need a powerhouse to stream internet tv.
i use a thunder port from my mac laptop to VGA in my telly. but its the same using thunder port to HDMI so a laptop can beam pictures direct into your TV via the PC channel on most bravia models
i know some of these ideas are quite far out even technical and its a little like throwing stones in the dark but maybe something i described could be useful to you at one point in the future i hope.
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How many time have you tried to play a flash video and you PC starts with all that 'there is a new version of flash player.' This is the problem, they are overkill its just not fair expecting people to constantly need to update. The old versions are technically fine, but adobe wont let them work, whats wrong with using an out of date flash player that can still do the job until its non functional because it acctually doesnt work not because they decide when it it shouldnt work.
this type of attitude to updates doesnt fly with streaming browsers they just cant keep up and its to be expected that some part of previous version have some functionality. Yes some streaming browsers partially support flash player but not to a level of reliability that is considered functional many go for months at a time without streaming flash player. you may not have noticed this on previous internet browsers but when flash is supported you have to wait for the latest build for it to be included that can take sometimes up to 3 years! They make way to much of a big deal over very little.
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