The only issue I can see in your animation is from the striped lines in the oven glass. I believe the "flickering" you're seeing is those lines are interacting with over edges/lines inside the oven or reflected in the glass and creative a moiré patter effect. Back in my print days, the only way to remove the patter was to alter the angles of things that are interacting. If a TV host makes the mistake of wearing a fine patterned jacket on air, the patter with interact with the pixels of the camera. This is way you will see mostly solid colors on TV or at least larger patterns.
One test you can do to see if I am correct, is to take your material on the oven door and rotate it several degrees and render a short test. If I am right, that flicker will either get better, worse or perhaps disappear but that is unlikely since the camera is moving and so the angles are constantly changing.
So my theory can easily tie in with @maru's idea of increasing the passes and/or render size. The more pixels, the smoother the result. There's a catch. You can render at 4k and it looks perfect, but when you sample down to HD or any online compression, you may re-introduce some of the flicker. Most likely, it will be less but also softer output overall which could be good or less good.
The rest of the scene seems smooth to me, even the sparkles on the stove burners are smooth. I believe there's a way to render just a portion of the frame. Maybe in that output, you can crank up the passes or what the others have suggested to reduce the render times.
