You have to go the oauth path. It’s annoying, but it’s doable. You also need to have your client_id approved by Amazon in order to use the API. http://advertising.amazon.com/API/docs/guides/authorization.
So 1) create an app in Login with Amazon
2) Get that client approved by Amazon (takes about 2-3 weeks)
3) Then you can implement the oauth flow to get a refresh token
4) use that refresh token to make a call to /profiles to get your accounts profile id
5) use the refresh token and profile ID to make calls to the API