A flow control assembly can be disposed in a wellbore and can include a membrane that can be perforated in response to a pressure, such as a setting pressure, from an inner area of a tubing. Subsequent to the membrane being perforated, fluid can be allowed to flow from an area external to the tubing to an area internal to the tubing. The membrane may remain closed during a packer setting operation and be perforated subsequent to the packer setting operation.