This may help give you an idea on how to make a divider for the tank.
New bettas can have bad eating habits (for lack of a better way to put it) the first few weeks after being purchased/brought home. They won't always eat regularly, or some won't eat at all for days/weeks.
Keep offering him the food, removing any uneaten after 10-15 minutes. He gets hungry enough, he will eat.
Keep an eye on him though, make sure he doesn't become clamped or lethargic - if you see him with his fins all pinched up, or isn't swimming around then you may have something to worry about. But for now, just give him time.. can change his food to New Life Spectrum or Omega One betta if he doesn't start eating in a week - see if maybe he changed his mind on whether or not he likes the food and is just being stubborn.. or you can be stubborn too and make him eat the food by offering only that. :)