That is an interesting question.
To answer this, you need to look at what Henry says, what he does, and what effects he has on others.
If you go by his words, he rejects standard or common views of morality. He doesn’t give conventional understanding of right and wrong much weight, if any. Instead, he continually praises beauty and pleasure. As such, Henry is a dandy, and represents the Aesthetic movement.
Despite this, he still shows some rudimentary sense of older values. He has friends, for example, and seems to care about what happens to them, and that’s not necessarily part of what a purely Aesthetic position would reveal.
He is also inconsistent. He says influence is a terrible thing, and that no one should be influenced by another or try to influence others. However, he spends a lot of time and energy to influence Dorian.
Ultimately, Henry is an entertainer, justifying his positions through his wit and the speed with which he delivers his comments.
To put all of those things together, Henry values pleasure, beauty, novelty, art, and style. He gives friendship some weight, but is also selfish and inconsistent. He rejects most standard morality.