The main argument in Joseph Butler's Fifteen Sermons preached at the Rolls Chapel regarding self-love and benevolence being compatible is that self-love is a manifestation of benevolence and, for that reason, they exist together.
Self love is defined as the desire of individuals to find themselves. This entails that we are willing and capable to accept our good and bad qualities as well as our strengths and weaknesses. Once all that is recognized, the next step is to find personal satisfaction and lead a happy life. The way to do this is by doing what we love to do since we now understand who we really are.
Benevolence is, according to Butler, the natural tendency of all human beings. In a dramatic contrast to what Freud would say from a modern perspective, Butler would argue that we are all, essentially, good. Hence, since we are all essentially good, self-love comes as one of the many ways to show such goodness. We, as benevolent people, will want to help others also lead a life of happiness. Rather than being selfish and contemptuous of other's well-being, we instead wish the best for all men and women that we meet and we aid them in the process of also finding themselves as individuals.