Thermal mass is of little use. I mean if you had an 8oz block of aluminum inside the flashlight with no way to get the heat out, it would take awhile to heat up but it'll still be hot. Well in theory if you had a block so huge it wouldn't heat up before the batteries ran down that would help, except no practical size of aluminum has a mass that would resist heating up for more than a few minutes when heated with 1W-5W.
Aluminum must be thick enough to conduct heat to the fins/case external cooling surfaces with minimal resistance. While the calcs are complicated, conducting heat over short distances with 1/16" thick aluminum is probably more than adequate. The edge of the sink has to make good contact with the case and that requires a thicker edge to increase contact surface. The center may require screw mounts and that requires a certain thickness to hold the threads and not distort under the pressure of the screws.
Copper is a superior material, nearly twice the thermal conductivity of aluminum. It's softer and somewhat more limited in minimal thickness due to mechanical stiffness. It's solderable which is really excellent for some emitters.
Anyhow most flashlight designs have no problem getting the needed thickness and trying to shave the sink just slightly thinner may have no practical benefit, since it might only gain a mm for all the trouble and questions.