Hi, my baby girl is 3-ish months old now. Honestly, I didn't let her sleep on a pillow, simply because I was afraid that she might suffocate herself as now as currently she is learning to flip over and prefer to sleep side way. I just fold a big towel and use it as a pillow. However, I do intend to provide her a pillow at a later stage e.g. when she finally manage to turn around on both sides.
P/S I do not believe that any pillow can help to prevent flat head.