While adding a light to my hallway, we found that a receptacle circuit for our dining room runs along the wall and behind my freezer. (We have a separate refrig. And freezer that sit side by side to look like a larger type). We had the freezer plugged into it, and the fridge plugged into another recept. Next to it that is not on the same line, and is likey to be the dedicated refrig. Circuit. Now we hardly ever have anything plugged into the dining room plug, and the light won't be on much, just to enter the house. Should we plug the freezer into the plug the refrig. Is in, or let it the way that its is? The light does dim when the freezer kicks in.

While a reefer and freezer do not draw much while running, there can be a slight chance that both can start at the same time, and the combined starting current can trip the breaker.

So I would not recommend having a freezer and reefer on the same circuit.

The lights blinking show the starting current, but does not cause any harm.

One observation I made, if your home was wired in the last 40 ish years, perhaps more, lights have not been allowed on dining room receptacle circuits, as dining rooms have been required to use 20 amp small appliance circuits, and no lights allowed.