Why do massive stars not undergo a helium flash I understand that for low-mass stars the helium flash occurs due to their degenerate helium cores. Thus the answer to this question is probably that more massive stars do not have a degenerate core, but I do not understand why they wouldn't. Due to their increased mass, I'd assume their central pressure is even higher, so surely their cores should also be degenerate?
After H burning has finished, the he mass of the He core gradually increases, as does its density and temperature.
Low-mass stars have denser cores when they reach a temperature at which He is ignited. The density is high enough that the electrons in the core are degenerate. In such conditions the heat from the nuclear reactions goes almost exclusively into raising the temperature of the He ions, but almost none goes to the degenerate electrons which have a very low heat capacity, yet dominate the pressure. This leads to a runaway increase in the nuclear fusion rate.
In higher mass stars the core is less dense when it reaches the He ignition temperature. This temperature is almost exactly the same as the ignition temperature for lower mass stars because of the very strong temperature dependence of the triple alpha reaction. The level of degeneracy depends on the ratio of density to temperature (it does not directly depend on the pressure).
At the lower densities in the higher mass stars, the electrons are not degenerate when He ignites and the heat capacity of the electron gas is higher than the ions (because there are more electrons than ions). In this case the heat from the nuclear reactions can effectively raise the pressure, doing work which expands the core and regulates the nuclear reaction rate.
See also https://physics.stackexchange.com/questions/174801/why-is-the-release-of-energy-during-the-he-flash-in-stars-almost-explosive