Optical trapping and manipulation of nanoparticles in integrated photonics devices have recently received increasingly more attention and greatly facilitated the advances in lab-on-chip technologies. In this work, by solving motion equation numerically, we study the trapping dynamics of a nanoparticle near a high-index-contrast slot waveguide, under the influence of water flow perpendicular to the waveguide. It is shown that a nanoparticle can go along different paths before it gets trapped, strongly depending on its initial position relative to the integrated waveguide. Due to localized optical field enhancement on waveguide sidewalls, there are multiple trapping positions, with a critical area where particle trapping and transport are unstable. As the water velocity increases, the effective trapping range shrinks, but with a rate that is smaller than the increasing of water velocity. Finally, the trapping range is shown to decrease for smaller slot width that is below 100 nm, even though smaller slot width generates stronger local optical force.