There are many types of leader and a flat organisation just means that you won't get to be a "type 1" leader, or an imposed leader if you will. That doesn't mean you can't rise to the position using skills and personality.
If you really want to go for leadership in your career look up some courses and books on the subject and talk to a mentor or even HR about developing a career plan.
Ideally, people are paid what they are worth - so that would imply there would be instances where people had the same title, but vastly different pay. The challenge always seems to be how to reliably determine who is really having more impact and who is positioning themselves to look like they are.
If you really want to go for leadership in your career look up some courses and books on the subject and talk to a mentor or even HR about developing a career plan.
Good luck!