Is there a frame story?
You need to start by thinking about what a "frame story" is before you can identify it. A frame story is a story that literally "frames" the main story, just as a frame "frames" a picture, either both at the beginning and the end or just the end or the beginning. Wuthering Heights, for example, is a classic example of this kind of tale, as the main story of Catherine and Heathcliffe is framed by the narration of Lockwood and his sojourn in the moors. Another example is The Turn of the Screw by Henry James, a chilling ghost story, which opens with a framing narrative describing a ghost-story competition before the main story of the haunting of two children begins.
Based on this definition there is no framing story to Lord of the Flies. The story begins with Ralph on the island and ends with the arrival of the navy, making both beginning and end an integral part of the narrative. There is no distancing of a central story through time and geography as there are in classic framing narratives.