A cooling system for a transition duct for routing a gas flow from a combustor to the first stage of a turbine section in a combustion turbine engine is disclosed. The transition duct may have a multi-panel outer wall formed from an inner panel having an inner surface that defines at least a portion of a hot gas path plenum and an intermediate panel positioned radially outward from the inner panel such that at least one cooling chamber is formed between the inner and intermediate panels. The transition duct may also include an outer panel. The inner, intermediate and outer panels may include one or more metering holes for passing cooling fluids between cooling chambers for cooling the panels. The intermediate and outer panels may be secured with an attachment system coupling the panels to the inner panel such that the intermediate and outer panels may move in-plane.