Is there a kingdom law or tradition of putting the kingdom arms on the hoist of a standard?

No, there is no Kingdom Law on the topic, but using the Kingdom Populace Badge is usually appropriate.

Please see Massaria’s post from discussion on the Blazons List on standards for Shires (and individuals) : October 2009

It is not appropriate to display the full Kingdom Arms, with wreath and crown, when the Crown are not physically present.

For more examples of standards than you can poke a stick at, go here

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