They do best in species only tanks due to the fact that they are nearly blind and have to sniff out food.
It has been done with bettas, but it also depends largely on the tank set up and the personality of the betta. You will also need to pick up plastic tweezers or a turkey baster to feed the frog directly.
They also need different types of food - frogs cannot eat fish flakes and the betta will ignore the frog pellets.
Best to just give the frog it's own tank with a few more frogs for company. A 10 gallon can house 5-6 frogs nicely and they are much more fun to keep in a group and watch their antics!