Hey Huvi, Shaq from the Support Engineering team here! 

It doesn’t look like our Oauth flow is compatible with what you’re looking to achieve. We also only support Oauth for public apps: https://developers.intercom.com/docs/build-an-integration/learn-more/authentication/setting-up-oauth

For this you would need to use the key pair option: https://docs.snowflake.com/en/developer-guide/snowflake-rest-api/authentication. 

I also found this other community post which may be useful to you: