Antennas are used by modern communication systems for a variety of purposes. Multiband antennas are proving versatile for most systems because of their efficient multi-functional services. The methods of slotting, defected grounds, stacking, metamaterials, reconfiguration, etc., which have been used over a long span of time to enable multi-frequency operation in antennas, have their own constraints. The Sierpinski Gasket fractal antennas are potentially the strongest contenders for implementing rapid multiband antenna design. This is because the multiple frequencies of these antennas result from the geometric self-similarity property of fractal, and can be influenced by the geometric parameters of the Gasket fractal. Plethora of investigations is reported in the literature on the scaling of Gasket height to generate multiple frequencies. Limited research is, however, available on the contribution of the flare angle design parameter of Gasket structures. Also, for practical applications, frequency is only one of several antenna-parameters, namely, return loss, bandwidth, gain, directivity, etc., that are required to be customized. In fact, using ways to quickly design Gasket antennas for multiple requirements would necessitate controlling reflection and radiation properties as well, which are associated with the antenna frequencies. In view of these concerns, the various transmission line feeding configurations of Gasket antennas have been explored in the current research effort to ascertain the contribution of various design characteristics that regulate the overall performance of these antennas. The novel insight presented into the establishment of input–output pairs of Gasket fractal antennas shall expedite the development of antennas with custom multiband properties.