Firefox, some problems
Well Firefox uses flash 11.2 and 11.2 doesn't support hardware acceleration so graphics are terrible. Chrome is supported in Linux, I use it. Also they could release Unity Tanki Online that uses the Web player and a standalone player and uses the same servers etc. It wouldn't be a third version.
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You are talking about several computer systems. What is yours?
Flash Player Version: 18.0.0.232
https://www.adobe.com/products/flashplayer/distribution3.html
Note: Windows users must download the “Internet Explorer”
and “Plugin-based browsers” installers.
Flash Player (Linux) Version 11.2.202.508
https://www.adobe.com/products/flashplayer/distribution3.html
Edge on Win10 does not use ActiveX version but its own Flash.