In modern times, electro-kinetics-based microfluidic pumping procedures find wide implementations in multifarious branches of biomedical and physiological manifestations. In this context, our main intention in this research work is to outline a mathematical framework for the hemodynamical characterization of blood circulation loaded with trihybrid nanoparticles inside an eccentric endoscopic arterial canal with a flexible wall under the interference of buoyancy and electro-osmotic forces. The subsequent rescaled equations are solved by employing an analytical approach with the help of Mathematica coding. The changes in the hemodynamical profiles in the endoscopic arterial duct against the preeminent parameters are overlooked via graphical demonstrations. Our graphical inspection proves that blood mobility across the endoscopic arterial tract gets more intense for elevated electro-osmotic parameter values and wall slip factor values. The use of unlike shapes of trihybrid nanoparticles attains the desired heat flow rate in surgical procedures. The lower temperature distribution is recorded for higher loading of trihybrid nanoparticles injected into the bloodstream. Overall, noteworthy findings of this modelling would find an effective way to design tools or devices for medication administration issues and electrotherapies.