Human immunodeficiency virus-1 reverse transcriptase (HIV-1 RT) is a heterodimeric DNA polymerase responsible for synthesizing double-stranded proviral DNA from the single-stranded RNA viral genome. In this work, we study the DNA polymerization dynamics of HIV-1 RT at the single molecule level using a hydrodynamic flow-stretching assay. In this assay, bead-tethered DNA molecules are surface immobilized inside microfluidic flow cells, and DNA templates are stretched by hydrodynamic forces. In this manner, we directly observe polymerization dynamics as a function of template DNA sequence for single enzymes. We observe the primer extension activity of HIV-1 RT on single DNA templates with a force-dependent DNA synthesis rate. In the low force regime, the average synthesis rate is 22 nt/sec. Furthermore, we observe transient enzyme stalling at specific locations within the single-stranded DNA template, and we demonstrate that enzymatic pause sites are in high correlation with hairpins in the DNA template. Finally, we present the hydrodynamic flow-stretching assay as a useful single molecule tool to study both specific and non-specific nucleic acid-protein interactions in a multiplexed and high-throughput format.