Nto which kingdom would you classify a newly discovered unicellular, eukaryotic organism that moves using a flagellum?

The answer is Protist. Oganisms in this group are referred to as unicellular "animal-like" protozoa. They are later classified into ciliated, flagellated, phagocytic, and spore-forming. This group is reserved for microscopic organisms while Protoctista groups multicellular eukaryote organisms such as slime molds.