The proposed high luminosity high energy Electron-Ion Collider (EIC) will explore the proton/nuclear structure in a wide Bjorken-x ($x_{BJ}$) and $Q^{2}$ phase space. Heavy flavor products are generated in initial collisions and have their hadronization influenced by the nuclear medium. Heavy flavor hadron and jet measurements at the future EIC will allow us to better constrain the nPDFs especially in the poorly constrained high $x_{BJ}$ region, precisely determine the quark/gluon fragmentation processes and directly study the quark/gluon energy loss within the nuclear medium. These measurements can constrain the cold nuclear medium effects for previous and ongoing heavy ion measurements at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). Silicon vertex/tracking detectors are essential to realize the heavy flavor and jet measurements at the EIC. Feasibility studies in simulation for proposed heavy flavor and jet observable with evaluated detector performance at the future EIC will be discussed.