This paper aims to measure the efficiency of urban street networks (a kind of complex networks) from the perspective of themultidimensional chain of connectivity (or flow). More specifically, we define two quantities: flow dimension and flow capacity, tocharacterize structures of urban street networks. To our surprise, for the topologies of urban street networks, previously confirmedas a form of small world and scale-free networks, we find that (1) the range of their flow dimensions is rather wider than theirrandom and regular counterparts, (2) their flow dimension shows a power-law distribution, and (3) they have a higher flow capacitythan their random and regular counterparts. The findings confirm that (1) both the wider range of flow dimensions and the higherflow capacity can be a signature of small world networks, and (2) the flow capacity can be an alternative quantity for measuring theefficiency of networks or that of the individual nodes. The findings are illustrated using three urban street networks (two in Europeand one in the USA).