This paper describes a flexible microstrip patch antenna that incorporates a novel multi-layer construction consisting of a liquid metal (eutectic gallium indium) encased in an elastomer. The combined properties of the fluid and the elastomeric substrate result in a flexible and durable antenna that is well suited for conformal antenna applications. Injecting the metal into microfluidic channels provides a simple way to define the shape of the liquid, which is stabilized mechanically by a thin oxide skin that forms spontaneously on its surface. This approach has proven sufficient for forming simple, single layer antenna geometries, such as dipoles. More complex fluidic antennas, particularly those featuring large, co-planar sheet-like geometries, require additional design considerations to achieve the desired shape of the metal. Here, a multi-layer patch antenna is fabricated using specially designed serpentine channels that take advantage of the unique rheological properties of the liquid metal alloy. The flexibility of the resulting antennas is demonstrated and the antenna parameters are characterized through simulation and measurement in both the relaxed and flexed states.