We investigate the $Tbar{T}$-like flows for non-linear electrodynamic theories in $D(=!!2n)$-dimensional spacetime. Our analysis is restricted to the deformation problem of the classical free action by employing the proposed $Tbar{T}$ operator from a simple integration technique. We show that this flow equation is compatible with $Tbar{T}$ deformation of a scalar field theory in $D!=!2$ and of a non-linear Born-Infeld type theory in $D!=!4$ dimensions. However, our computation discloses that this kind of $Tbar{T}$ flow in higher dimensions is essentially different from deformation that has been derived from the AdS/CFT interpretations. Indeed, the gravity that may be exist as a holographic dual theory of this kind of effective Born-Infeld action is not necessarily an AdS space. As an illustrative investigation in $D!=!4$, we shall also show that our construction for the $Tbar{T}$ operator preserves the original $SL(2,R)$ symmetry of a non-supersymmetric Born-Infeld theory, as well as $mathcal{N}=2$ supersymmetric model. It is shown that the corresponding $SL(2,R)$ invariant action fixes the relationship between the $Tbar{T}$ operator and quadratic form of the energy-momentum tensor in $D!=!4$.
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