access_token not added as claim on the ClaimsIdentity after login to asp.net app

If you are following https://auth0.com/docs/quickstart/webapp/aspnet-owin/03-storing-tokens, that’s the correct place to start.
Are you setting SaveAccessToken to true? If so, does this expression returns null?

string accessToken = claimsIdentity?.Claims.FirstOrDefault(c => c.Type == "access_token")?.Value;

Which version of the OWIN package are you using?