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In this paper we develop the homological properties of the $(\mathcal{L},\mathcal{A})$-Gorenstein flat $R$-modules $\mathcal{GF}_{(\mathcal{F}(R),\mathcal{A})}$ proposed by Gillespie. Where the class $\mathcal{A} \subseteq\mathrm{Mod} (R^{op})$ sometimes corresponds to a duality pair $(\mathcal{L},\mathcal{A})$. We study the weak global and finitistic dimensions that comeswith $\mathcal{GF}_{(\mathcal{F}(R), \mathcal{A})}$ and show that over a$(\mathcal{L}, \mathcal{A})$-Gorenstein ring, the functor $-\otimes _R -$ isleft balanced over $\mathrm{Mod} (R^{op}) \times \mathrm{Mod} (R)$ by theclasses $\mathcal{GF}_{(\mathcal{F}(R^{op}), \mathcal{A})} \times\mathcal{GF}_{(\mathcal{F}(R), \mathcal{A})}$. When the duality pair is$(\mathcal{F} (R), \mathcal{FP}Inj (R^{op}))$ we recover the G. Yang's resultover a Ding-Chen ring, and we see that is new for $(\mathrm{Lev} (R),\mathrm{AC} (R^{op}))$ among others.

$(\mathcal{F},\mathcal{A})$-Gorenstein flat homological dimensions