Chlamydomonas, Chlorella are present in Kingdom Protista as well as Plantae under division algae.
In which kingdom they correctly belong to?
It is generally accepted now that Chlorophyta are Plantae (see here). They are more closely related to plants than any other group of organism. Protist is a kind of basket term for any eukaryotic unicellular organism that is not an animal, fungi or a plant which is a rather exclusionary definition.
Personally, I think the kingdoms are pretty 'macro' oriented and do not really capture the diversity well of unicellular organisms. If you want to see a bunch of elderly scientist shout at each other over what appear to be arbitrary distinctions, I highly recommend attending the taxonomy session of any unicellular conference