I just changed the settings in Kibana -> Advanced Settings and looked in the developer console to see what was going on and below is what it was doing.
POSThttp://localhost:5601/api/kibana/settings
body{"changes":{"theme:darkMode":false}}
This doesn't seem like the correct way to do it but it also doesn't look like it's part of the documented API. So.... ya, it works but use at your own risk and could break in future versions.
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