You can pre-generate the HD cache, which will prevent flickering by locking the lighting to a single solution. However, that also means that the indirect lighting won't really update to accommodate for moving objects, so that's not going to work. Corona does not have temporal interpolation like V-Ray does (where you pre-generate one cache per frame, and then blend between them).
You can either do full path tracing for both primary and secondary bounces (PT-PT), which is guaranteed flicker-free. However, it is also significantly noisier than PT-HD Cache.
However, I've actually had some success with PT-HD. The trick seems to be to turn up the sensitivities. I did one test where I doubled the directional and normal sensitivities from their defaults, and I set position sensitivity to 80. That rendered completely flicker-free. Turning up the HD cache accuracy might also help.
For post-processing, the one I've had best success with is
RE:Vision Effects' DE:Noise, but I'm sure the Red Giant product works well too. This can help both with per-pixel noise from the path tracing, as well as the flickering from the HD cache. If you are able to render out motion vectors and have access to either Fusion or Nuke or some other such high-end compositing hardware, you can use the motion vectors to apply even better deflickering/denoise in post.
Finally, if you're rendering an animation, use
bucket mode, not progressive! You get much better results that way because the bucket mode can sample some areas more than others, which can really help deal with difficult noise. Progressive mode always samples all pixels by the same amount, which can be suboptimal.