When you use incognito or private mode, Chrome doesn't block third-party cookies by default. However, keep in mind that this mode is designed for private browsing and doesn't save your history, cookies, or site data when you're done.
Before you go deep into settings, verify that third-party cookies are the culprit.
This is the . You tell Chrome: “Only unblock third-party cookies when I am on trusted-site.com .” This preserves privacy everywhere else.