This paper presents Tinker Tales, an interactive storytelling framework in the format of a board game, designed to support both narrative development and AI literacy in early childhood. The framework integrates tangible and speech-based interactions with AI through NFC chip-attached pawns and tokens, along with a speaker and microphone. Children select and define key story elements-such as characters, places, items, and emotions-using the pawns and tokens, providing further details to the AI and receiving proper assistance, similar to how adults prompt AI for specific tasks (e.g., writing). For evaluation, several game sessions were simulated with a child AI agent, and the quality and safety of the generated stories were assessed from various perspectives. This work highlights the potential of combining physical and digital elements in AI literacy, offering a safe and engaging way for children to learn how to effectively collaborate with AI.