It's using RSA with key length of 2048 bits [1], and one can assume that both prime factors have equal bit length [2] i.e. 1024 bits each, and so the size of all the other private components can be derived from that. I don't know what OpenSSL's in-memory format is for this data, I suppose therein lies a good part of the challenge!

[1] https://www.ssllabs.com/ssltest/analyze.html?d=cloudflarecha...

[2] https://github.com/openssl/openssl/blob/master/crypto/rsa/rs...