The characters in The Picture of Dorian Gray are not necessarily round and complex. For a character to be round and complex it needs to change throughout the plot as a result of the different dynamics that take place in the story. Dorian Gray, Lord Henry, and Basil remain the same from beginning to end. Therefore, one can conclude that, with the exception of a few minor changes in their characteristics, all three characters are quite stereotypical and somewhat flat.
Here is why:
If you start your analysis with Lord Henry Wooton, you can immediately notice how his character is no different than Wilde's other dandies from other works such as Lord Goring or Lord Darlington. The role of Lord Henry is to corrupt Dorian Gray and to show him a life of sin without remorse. It is clear that Lord Henry remained the same throughout the novel and did not change as a consequence of anything.
Dorian Gray never changed either. Aside from the fear of seeing his picture, he never attempted to change his immoral ways. When he ripped the picture (and killed himself as a result), he did not do it out of remorse for the things that he did. He did it because he was too scared of the picture and was sick of it, but not of his sins.
Basil never changed either. He is stereotypical of the artistic classes in Victorian London, as he said to Lord Henry himself. He is the typical "entertainment" of the upper classes, who opted to befriend artists and become their patrons to make up for their own lack of intelligence and charisma. His devotion to Dorian never changed either. If anything, it intensified through time to the point of trying to protect Dorian from the awful things said about him in London. His love for Dorian led to his death (by Dorian's own hand).
Therefore, you can say that the characters in The Picture of Dorian Gray are flat and stereotypical, but also interesting, full of charm, and truly classic.