Which kingdom is completely composed of unicellular organisms that are prokaryotic

Prokaryotes are single-celled organisms with no nucleus, and so this would make bacteria a prime example. Therefore, depending upon the system being used, the kingdom that contains single-celled prokaryotes could be Monera, or the combination of Archaeobacteria and Eubacteria.

The kingdom systems, which were previously taught in high school, consisted of a 5-kingdom system which was later expanded to 6. The 5- kingdom  included Animals, Plants, Fungi, Monera and Protists. The 6- kindgom system expanded Monera into Archaeobacteria and Eubacteria.

The "kingdom" system of classification is now generally not recognized as a valid or helpful way of classification, at least not according to modern evidence. It tends to be "paraphyletic", meaning that it describes relationships which do not match the evolutionary relationships of the organisms being described, and tends to favor human conventions rather than biological evidence. Kingdoms have generally been replaced by "domains" in terms of organizing relationships between organisms, referring to the prokaryotes, eukaryotes, and archaea, based on genetic and protein data.

Bacteria because they only have a small amount of cells, mostly just one which makes them unicellular and they do not have a nucleus which makes them prokaryotic.