Modern electronics continue to shrink down the sizes while becoming more and more powerful. To improve heat dissipation of electronics, fillers used in the semiconductor packaging process need to possess both high electrical and thermal conductivity. Graphene is known to improve thermal conductivity but suffers from van der Waals interactions and thus poor processibility. In this study, we wrapped silver microflakes with graphene sheets, which can enable intercoupling of phonon- and electron-based thermal transport, to improve the thermal conductivity. Using just 1.55 wt % graphene for wrapping can achieve a 2.64-times greater thermal diffusivity (equivalent to 254.196 ± 10.123 W/m·K) over pristine silver flakes. Graphene-wrapped silver flakes minimize the increase of electrical resistivity, which is one-order higher (1.4 × 10-3 Ω·cm) than the pristine flakes (5.7 × 10-4 Ω·cm). Trace contents of wrapped graphene (<1.55 wt %) were found to be enough to bridge the void between Ag flakes, and this enhances the thermal conductivity. Graphene loading at 3.76 wt % (beyond the threshold of 1.55 wt %) results in the significant graphene aggregation that decreases thermal diffusivity to as low as 16% of the pristine Ag filler. This work recognizes that suitable amounts of graphene wrapping can enhance heat dissipation, but too much graphene results in unwanted aggregation that hinders thermal conducting performance.