The boy didn't think he had any reason to need to "escape." In his imagination, he was Red Chief, the Indian who was in charge of the two captives, Old Hank and Snake-eye. Obviously he couldn't abandon his prisoners by leaving his hideout cave until they had both been properly punished - Old Hank was "to be scalped at daybreak" and Snake-eye would "be broiled at the stake at the rising of the sun."
Given the tremendous adventure of it all, given his nine-year-old enthusiasm and non-stop energy, given the fact that he had never had the opportunity to go camping with two men who did whatever they could to go along with his ideas - why would he want to leave?
He was having too much fun.