Does experience at a startup for a couple of years increase the chances of getting into a good Ph.D programme in a US university?
The answer to all of these questions and more is going to be: Maybe. 

Experience will help, but testimonial in the form of reference letters will be better. If you work at this company and it gets you a dynamite reference letter, testifying to your skill, it may help you. On the flip side, for a PhD, skill may not be sufficient--- for a PhD your research background (what you already have) may be much more important than the work experience.