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Kiselev metric in the static and rotating form is widely used to test different aspects of the dark energy (DE) effects. We consider a DE Kiselev spacetime, predicting the reduction to the Kerr black hole (BH) solution under suitable conditions on the DE parameters and in this frame we study the effects of the dark energy on BHs and disks accretion. Elaborating a close comparison with the limiting vacuum Kerr spacetime, we focus on thick accretion disks around the central BH in the Kiselev solution, both co-rotating and counter-rotating with respect the central BH. We examine different aspects of BH accretion energetics by focusing on quantities related to the accretion rates and cusp luminosity, when considered the DE presence, related to the pure Kerr central BH. Our findings show that in these conditions heavy divergences with respect to the vacuum case are expected for the DE metrics. A known effect of the Kiselev metric is to lead to a false estimation the BH spin, we confirm this characteristic from the fluids dynamics analysis. Remarkably our results show that DE is affecting differently the accretion physics, and particularly the accretion rate, according to the fluid rotation orientation with respect to the central spinning attractor, leading in some cases to an under-estimation of the BH spin mass ratio. These contrasting aspects emerging in dependence on the fluids rotational orientation can be a distinguishing general DE feature which could lead to a revised observational paradigm where DE existence is considered.