There was no actual flashing used on the apron of the chimney. All the installer did was use tap-con screws to connect the EPDM roofing to the brickwork and seal it with caulking. Contrary to what some installers believe, caulking is not flashing. It can be used to augment flashing, but should not be relied upon as the only type of flashing. Weather and freeze-thaw cycles weaken and deteriorate the caulking compound adhering the flashing to the chimney. It may work to keep water out for a while, but eventually it will crack and fail.
A better installation method would have been to bring the EPDM material up onto the brickwork at least 6 inches, use a termination bar with sealant to attach the EPDM to the brickwork, and then use metal counter flashing with an underbroken top hem for a friction fit in a reglet cut into the brickwork. Caulking would be used to help seal the reglet opening where the counter flashing was inserted.
As with all caulking applications, periodic inspection of the caulked areas should be performed. How often this is performed depends upon many factors such as the quality of the caulking used, the type of caulking used (latex, vinyl latex, siliconized acrylic, pure silicone or butyl rubber), exposure to heat and sunlight, and the condition of the substrate.