Hello and welcome!
Some bettas take longer to acclimate to a new home then others. I've heard of members with new bettas going for a week or more without food after their arrival, but that's fairly rare. He may just need more time to adjust. However, I personally would go ahead and purchase some new food, he may just be a picky eater. There are a lot of different foods you can try, pellets (42% protein or higher) and frozen (not freeze dried) foods like mysis shrimp, brine shrimp, bloodworms and daphnia, and even live insects like wingless fruit flies. Just make sure you take out any uneaten food from his tank. ^^
Good luck! :D