Quantum spin Hall insulators (QSHIs) make up a class of two-dimensional materials with a finite electronic band gap in the bulk and gapless helical edge states. Some of the phenomena that can be hosted in these materials, from one-dimensional low-dissipation electronic transport to spin filtering, could be promising for many technological applications in the fields of electronics, spintronics, and topological quantum computing. Nevertheless, the rarity of two-dimensional materials that can exhibit nontrivial topological order at room temperature hinders development. In the publication, we report on our screening of a comprehensive database we recently identified of 1825 monolayers that can be exfoliated from experimentally known compounds to search for novel quantum spin Hall insulators. In this entry we provide the AiiDA database with the calculations of the DFT band structures (both with and without spin-orbit coupling) and the DFPT phonon dispersions for the QSHI candidates that we identify. All the data are also displayed in the dedicated DISCOVER section "2D topological insulators" https://www.materialscloud.org/discover/2dtopo/dashboard/ptable .