That is depends on person. I barely use '까먹다'. We don't use '까먹다' for documents and business. By the dictionary, '까먹다' is a bit vulgar expression. ex)She often uses vulgar language. In addition, '깜빡하다' meaning is shorter time. (나는) 깜빡하고 집에 열쇠를 두고왔다. (나는) 친구에게 전화하는 것을 깜빡했다. We use '잊다' for both, long and short. (나는) 그녀를 잊었다. (O) (나는) 그녀를 깜빡했다 (X) (If you are busy to shop, then forgetting to care your daughter... it could use.) (나는) 숙제하는 것을 잊었다. (O) (나는) 숙제하는 것을 깜빡했다. (O) I think, '까먹다' is also for shorter time... It is complicate :)

Both are used very often, however, compare to 까먹다 vs 잊다 까먹다 more used. 까먹다 sounds bit slang but not slang actually. It's one of standard verb. Also, you can use 깜빡하다 too