The flux linkage per unit length will be the magnetic flux through the area bounded by the two dotted lines and the wires. Since the wires are symmetric about this area, you may calculate the flux linked from just one wire and then double. The formula found for the magnetic field about a long wire should be used here.
The area of linkage can be spanned with the infinitesimal element shown, varying r from a to d-a. In using these limits of integration, we are staying outside the wires; the magnetic flux linked inside the wire may also be included, but be sure to use the correct expression for the magnetic field inside the sire.