Actually, I think that most of the time being inclined to be selfless has a higher chance of leading you to happiness than being inclined to be selfish. But what really matters is how you see yourself, and how you think others see you. Both inclinations can lead to unhappiness with certain personalities and environments. If you are a selflessly inclined person that is around too many selfishly inclined people, you may get taken advantage of. If you are a selfishly inclined person that is around too many selfless people, you may become guilty because you are taking advantage of them. But in both situations if you don't mind when others see you as a tool and use you, or if you don't mind knowing you are using others, you can be happy in either situation. For most people there is a happy middleground. But much more often people will be happier being selfless because other people will be inclined to like them, and they will like themselves for being selfless. The person who genuinely does not care at all what other people think of them is incredibly rare. Most likely, the most selfish person you've ever met still does care a bit about what at least someone thinks of them.
A selfless person is selfish at their core, but they behave and think in a way that allows themselves and everyone else to forget about that reality. In my life I plan to behave selflessly, but I know and accept that I am doing that for a selfish reason.