Hey there,
I found this comment in another thread that seems like it should work for your needs, though it might end up providing all Custom Fields.
Notably, we do provide endpoints that integrations like Zapier can utilize on their end to retrieve Contact custom fields and associated data for you:
https://developer.infusionsoft.com/docs/rest/#operation/retrieveContactModelUsingGET
https://developer.infusionsoft.com/docs/rest/#operation/listContactsUsingGET
Cheers,
Mearl