Can I build a DH private key from an OpenSSL configuration file?

Yes, you can build a DH private key from an OpenSSL configuration file, if you know the components of the key, as shown in the test below:

C:\Users\fyicenter>type asn1_dh_pri_key.cnf
asn1 = SEQUENCE:dh_pri_key

[dh_pri_key]
version    =INTEGER:0
algorithm  =SEQUENCE:dh_alg
private    =OCTWRAP,INTEGER:0x4233D0A221A766BA2CE0492F2B8F6A822BE38CF33E\
3A6850C806C6031D78457E

[dh_alg]
algorithm =OID:dhKeyAgreement
parameter =SEQUENCE:dh_param

[dh_param]
prime      =INTEGER:0x8B58E1395DF5CF48DA87B088C6525EFF4AECBDA5C269EF2378\
A31A4A62B1647B
generator  =INTEGER:0x02

C:\Users\fyicenter>\local\openssl\openssl 
   asn1parse -genconf asn1_dh_pri_key.cnf -noout -out dh_pri_key.der

C:\Users\fyicenter>\local\openssl\openssl 
   pkey -in dh_pri_key.der -inform DER -text -noout
DH Private-Key: (256 bit)
    private-key:
        42:33:d0:a2:21:a7:66:ba:2c:e0:49:2f:2b:8f:6a:
        82:2b:e3:8c:f3:3e:3a:68:50:c8:06:c6:03:1d:78:
        45:7e
    public-key:
        4c:c9:c9:4c:eb:5b:13:f2:b4:b3:ab:b9:f2:0c:b8:
        30:ff:c3:bb:5d:c6:42:8c:08:b1:8c:f3:e5:30:19:
        08:ad
    prime:
        00:8b:58:e1:39:5d:f5:cf:48:da:87:b0:88:c6:52:
        5e:ff:4a:ec:bd:a5:c2:69:ef:23:78:a3:1a:4a:62:
        b1:64:7b
    generator: 2 (0x2)

⇒ OpenSSL "ans1parse" - DH Public Key in ASN.1 Structure

⇐ OpenSSL "ans1parse" - DH Private Key in ASN.1 Structure

⇑ OpenSSL "ans1parse" Command

⇑⇑ OpenSSL Tutorials