BB has already given its answer on Flash support in browsers: it has given us a standalone client which has its own flash embedded therefore it does not matter what the browser makers do.
We will always have a game to play whatever happens to Flash. As for re-writing to HTML5, it will be a big job and will require re-writing large parts of the game, some things may not even be possible in HTML5 versus Flash. I am going through a similar process at work migrating our product from Silverlight to HTML5. I have played this game since 2012 and I rarely get lag, the only times I have noticed server based lag is during busy events but those days have not been seen for a long while. I play the game in the standalone client, it is stable and 'lag' free. A lot of what people consider to be lag is actually their own PC resource issues such as processes consuming disk or processors, it doesn't matter how fast your PC is if there's something errant going on behind the scenes. The only time I get booted is when I leave it idle minimised, same as the browser does, I would question if that is not by design.
When Flash reaches EOL there will be a notice period of at least a few years and even then there will be ways to continue using Flash in browsers, exactly as there has been for Silverlight, not sure what the fuss is about.
Some of the things people are complaining about such as time it takes to queue/de-queue items are semantics of the client-server environment/deficient functionality, not anything at all to do with flash. If BB gave you a button that de-queued all items in the queue except the currently building one, it would need to talk to the database once, not once per item. That is just inadequate design, not lag.
If you're playing the game in a browser, do yourself a favour and install the standalone client. Most of the 'Flash' issues are caused by Flash objects on other browser tabs you have open at the same time as playing.