Combined plastic flow and strain-induced phase transformations (PTs) under high pressure in a sample within a gasket subjected to three dimensional compression and torsion in a rotational diamond anvil cell (RDAC) are studied using a finite element approach. The results are obtained for the weaker, equal-strength, and stronger high-pressure phases in comparison with low-pressure phases. It is found that, due to the strong gasket, the pressure in the sample is relatively homogenous and the geometry of the transformed zones is mostly determined by heterogeneity in plastic flow. For the equal-strength phases, the PT rate is higher than for the weaker and stronger high-pressure phases. For the weaker high-pressure phase, transformation softening induces material instability and leads to strain and PT localization. For the stronger high-pressure phase, the PT is suppressed by strain hardening during PT. The effect of the kinetic parameter k that scales the PT rate in the strain-controlled kinetic equation is also examined. In comparison with a traditional diamond anvil cell without torsion, the PT progress is much faster in RDAC under the same maximum pressure in the sample. Finally, the gasket size and strength effects are discussed. For a shorter and weaker gasket, faster plastic flow in radial and thickness directions leads to faster PT kinetics in comparison with a longer and stronger gasket. The rates of PT and plastic flows are not very sensitive to the modest change in a gasket thickness. Multiple experimental results are reproduced and interpreted. Obtained results allow one to design the desired pressure-plastic strain loading program in the experiments for searching new phases, reducing PT pressure by plastic shear, extracting kinetic properties from experiments with heterogeneous fields, and controlling homogeneity of all fields and kinetics of PTs.