Efficient capture of single-stranded DNA (ssDNA) is crucial for high-throughput sequencing, which influences the speed and accuracy of genetic analysis. Electrophoresis (EP) and electro-osmotic flow (EOF) have a significant impact on the translocation behavior of ssDNA through the nanopore. Experimentally, dynamically tracking these two effects remains challenging, and conventional numerical methods also struggle to capture their dynamic properties in the presence of DNA. We use all-atom molecular dynamics (MD) simulations to study how do EP and EOF play a role in the capture of DNA under different surface charge densities and graphene layer numbers. Our findings indicate that positive surface charge densities work together with electrophoretic forces (FEP) to enhance the EOF, resulting in rapid and efficient ssDNA capture with improved rates of up to 88% and reduced capture times. Electro-osmotic force (FEOF) substantially enhances capture efficiency by not only lowering the energy barrier for ssDNA translocation through the nanopore but also increasing the probability of ssDNA locating and aligning with the pore entrance. Negative charges create a repulsive electrostatic environment. Along with the opposing EOF, this lowers the chances of capture. Additionally, we found that an increased number of graphene layers can shield internal electric fields, affecting ssDNA capture negatively by tempering the effects of EOF. This research highlights the importance of precise control over nanopore surface charge and layers to optimize the performance of graphene nanopore sequencing technologies, offering potential avenues for significant advancements in genomic sequencing.