If American Express pulled a credit report in connection with this application, Chase would be able to see that you applied for "something" recently. However, American Express does not report business card accounts to personal credit bureaus, which means Chase will not know the outcome of the application, and it is unlikely to affect a Chase application unless you have several other recent inquiries.
Thanks. That leads me to another question. Is there such a thing as a business credit report or business credit score? Would Chase even be able to know that I have a business credit card with Amex, and how?
As a follow-up, I opened the Chase United Explorer in March 2023 and the Chase Marriott Boundless in November 2023. Yikes, that's three Chase cards in one year, two being personal and one being business. Knowing that, would that affect my chances?