  In this letter, we investigate the deformation of the ModMax theory, as a
unique Lagrangian of non-linear electrodynamics preserving both conformal and
electromagnetic-duality invariance, under $T\bar{T}$-like flows. We will show
that the deformed theory is the generalized non-linear Born-Infeld
electrodynamics. Being inspired by the invariance under the flow equation for
Born-Infeld theories, we propose another $T\bar{T}$-like operator generating
the ModMax and generalized Born-Infeld non-linear electrodynamic theories from
the usual Maxwell and Born-Infeld theories, respectively.
