By harnessing biochemical signaling and chemotaxis, unicellular slime molds can aggregate on a surface to form a long, vertical stalk. Few synthetic systems can self-organize into analogous structures that emerge out of the plane. Through computational modeling, we devise a mechanism for assembling tower-like structures using microcapsules in solution as building blocks. In the simulations, chemicals diffusing from a central patch on a surface produce a concentration gradient, which generates a radially directed diffusioosmotic flow along the surface toward the center. This toroidal roll of a fluid pulls the microcapsules along the surface and lifts them above the patch. As more capsules are drawn toward the patch, some units are pushed off the surface but remain attached to the central microcapsule cluster. The upward-directed flow then draws out the cluster into a tower-like shape. The final three-dimensional (3D) structure depends on the flow field, the attractive capsule-capsule and capsule-surface interaction strengths, and the sedimentation force on the capsules. By tuning these factors, we can change the height of the structures that are produced. Moreover, by patterning the areas of the wall that are attractive to the capsules, we can form multiple vertical strands instead of a single tower. Our approach for flow-directed assembly can permit the growth of reconfigurable, 3D structures from simple subunits.