You can see the request in the network tab when you navigate to a user profile like https://discuss.flarum.org/u/clarkwinkelmann/discussions
(I omitted the list of includes, they are optional if the default includes contain the data you need)
The relevant search gambit is
author:username. It will return discussions that have been started by the given user.
EDIT: and if you are using my Wordpress extension and don't have access to the Flarum username or ID, here are some solutions to get it in the first place https://kilowhat.net/flarum/extensions/wordpress#third-party-integrations