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I just looked at the new streaming page served source with a view to hack it and reference some objects back to BATC but will see.
Hopefully something can be provided, even it its a vanilla page with just the stream screen, so we can embed (or iFrame), into out pages for the time being.
With a both of webjiggery (new technical term), you can have this too! Happy to post details here if of interest. It has room for improvement but sure it will help some.
My temporary RILGER Repeater Site as an example http://rilges.org.uk/ This is displaying my test Dashboard. As I used HTML5, it will take around 30 seconds to load.
create a css file: stream.css
Add the below line in the webpage <head> section
<link rel="stylesheet" type="text/css" href="stream.css">
Add the below to your webpage
<div style="position: relative;width: 476px;height: 305px;overflow: hidden; left:-25px">
<iframe src="https://batc.org.uk/live/g8puo" scrolling="no" frameborder="no"></iframe>
The problem using flash is the need of users to enable the BATC website, hence why I took the HTML 5 route.
Hope this is of interest.