At the beginning of section 3 he defines a bicategory of spans from A to B in any bicategory, and given finite bilimits, essentially describes how to construct what one might call an "unbiased tricategory" of spans (of course, the definition of tricategory didn't exist at the time).
He doesn't give any details of the proofs, but one could probably construct a detailed proof from these ideas without much more than tedium. I don't know whether anyone has written them out.
One amusing thing about the tricategory of spans in a 2-category, with composition by iso-comma object, is that it is barely a tricategory. Binary composition is associative up to iso; it is only the unitality which is really up to equivalence. Something similar happens if you define a tricategory of biprofunctors. Richard