This post looks old so for newer users needing to update the client requests.
If using the most up to date spring security stuff, it will use a webclient in the backend to actual talk with the Reddit auth service. You will need to follow the instructions here https://docs.spring.io/spring-security/reference/reactive/oauth2/index.html#oauth2-client-customize-web-client, passing in the customized WebClient that sets the default header to the oauth clients to use when making the request.