Yes, selfishness is compatible with kindness, because selfishness itself may not be evil and secondly, there is no contradiction between selfishness and kindness. In fact, a kind person who is nice to the other person may do so out of his selfish desire, like whether a person wants to die for his country, or whether a mother is kind to her child; I believe a person is kind or friendly to other people because of his selfish desire. So, selfishness is compatible with kindness.
To add, selfishness is different to responsibility. Responsibility is doing what you do want to do. But selfishness is doing what he wants to do. So if a person wants to help people, he has selfish desire and therefore selfishness is compatible with kindness.
Now, German philosopher Kant was more in favour of responsibility than selfishness. He is treating humans maybe like a heartless machine. But to me, selfishness is more important than responsibility, because we are humans. I do not agree with Kant's moral idea.