An inflatable packer assembly can include an inflatable seal element having an internal inflation chamber, a flow passage extending longitudinally through the inflatable packer assembly, a flow restrictor between sections of the flow passage, and a flow controller that selectively permits and prevents fluid communication between the inflation chamber and each of the flow passage sections. The flow controller changes from a deflate configuration to an inflate configuration in response to an increase in flow rate through the flow passage. A method can include connecting an inflatable packer assembly in a tubular string, so that a longitudinal flow passage of the tubular string extends through the inflatable packer assembly, and a flow restrictor restricts flow between sections of the flow passage, and inflating an inflatable seal element of the inflatable packer assembly while fluid flows between the flow passage sections via the flow restrictor.