Hi Andrew,
You can use the OnChange option to apply the boolean values to multiple booleans.
Check the example below where checking the checkbox, it will trigger an action that will apply the selected value (Boolean local variable in my case) to multiple fields:

And then the screen action assigning the value to the multiple variables to be sent to the database later:

If you want to store it immediately on the database, you would just need to call the corresponding Create, Update or CreateOrUpdate action for the record.
Hope it helps.
Regards,
João