May you please give the direct quotation of what the clone said in Battlefront 2? I think I know what you're referencing, but I just want to be sure. I just want to say that even if the clones did know about Order 66, Sidious probably put another order in their chips that commanded them not to tell the Jedi.
That Sideous could say "Execute order 66" and the Clones all immediately knew what that meant makes it obvious that they knew about it.
Do you think about these questions before you ask them?
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"The Daemon lied with every breath. It could not help itself but to deceive and dismay, to riddle and ruin. The more we conversed, the closer I drew to one singularly ineluctable fact: I would gain no wisdom here."
Considering that it's in Republic law, I'm sure even some Jedi knew about it. They however could not know that Sidious would use it to his advantage. At least, not until too late.
The Clones did not know about the Order. Its pre-programmed secretly into the bio-chip. They are literally programmed like droids in that regard. That's why fives flipped the **** out when Sidious told him that he planned to kill all the Jedi.