Cloudflare support responded to me (in a private ticket) that most of the times this is caused by a mismatch in certificate and private key. In my case this wasn’t the case.
I turned out that one of the root certificates was not thrusted by Cloudflare.
I figured this out with the help of a tip from Cloudflare support: When you select “Bundle method” as “User Defined”, the certificate will be uploaded without error (at least if the certificate and key matches and are in the correct format). I then saw an SSL error in the browser of my website. When inspecting the certificate in the browser I saw that one of the root certificates was unthrusted.