In this article, we present a novel implementation of the equilibrated flux, the key ingredient in designing a p-robust error estimator. Our algorithm involves two primary loops: one on mesh cells and one on nodal patches. The loop on cells provides a setup phase that allows to reduce memory allocations for the potentially more costly loop on patches. Both of these loops involve mutually independent operations and are therefore amenable to parallelization strategies. We present numerical results of both the correctness of our implementation as well as evidence of the speedup due to parallelism. Our implementation is available as a registered Julia package under an MIT open source license.