I feel content outside of the regular narrative flow that is longer than about a page should generally be placed in a separate chapter (or section for shorter fiction), especially when such content is included multiple times within a novel.
Frame stories would generally be exceptions to this guideline since the outer story fragments are typically very short. Including a short portion of the outer story at the beginning of an inner story chapter
The transition to the inner story (at the end of the outer story) may include a small part of the beginning of the included story. This gives the chapter transition more of a dream-blur effect and reduces the separation between the narrative components. If the inner stories are meant to reveal aspects of the protagonist of the outer story, this might be preferred, particularly if the protagonist is specifically sharing his heart. This form of transition would work best if the author of the inner story is reciting the inner story or at least present waiting for the story to be read.
If the inner story is being read independently, a stronger transition would generally be desired to separate the reader in the outer story from the story itself. (Exceptions would include when the story is meant to be more personal to that reader and when the impression of an immersive narrative is intended.) Giving such strong transition story within a story chapters the titles of the short stories would help clarify that they are not part of the outer story.
If the inner story is being read by more than one reader, such a strong transition may be especially appropriate, though it could also be effective to use a fragment at the end of multiple chapters to show how different readers are coming to the story from their individual perspectives.
This introduces the issue of where to place the body of the story. Placing it immediately after the first reader's chapter allows the inner story's content to interact with the context of second reader (e.g., an upbeat inner story might be just what the second reader needs after the stressful experiences preceding the reading). Placing it after the last reader's chapter increases anticipation (which can lead to disappointment if the inner story is weak, though that disappointment might be intentional). Placing the inner story in the middle would bind it more closely to the readers in the adjacent outer story chapters and could be used to reinforce differences in how the inner story affects the different readers; the readers before the story are in some sense coming to the story afresh while the real-world reader's knowledge of the inner story will influence how the later chapters are viewed.
Obviously an inner story within a shorter work that does not have chapters could use section breaks. Because section breaks are weaker than chapter breaks, a greater sense of relation is implied, potentially requiring more explicit separation in the text itself if the inner story is meant to be more distinct from the reader. On the other hand, using section breaks would facilitate the use of subtle links between the outer and inner stories. In a novel, using section breaks could be effective for infrequent inner stories when the adjacent reader is meant to be particularly close to the story.