In the story I plan to write each chapter is its own self contained story, I'm trying to figure out how to link them back to the main story without it being clunky and feeling like I just stitched together a bunch of separate stories. How would I do this right?
That is an artistic question and therefore something that is very hard to help with. I've seen some people use, for example, an image or metaphor at the end of each scene. On the other hand it may be more practical and everything takes place in the same location, so you merely wrap up in a matter-of-fact way in a place the reader will recognise from an earlier story.
Are the characters or locations the same? Does all the stories revolve around the same theme? I have several stories written like episodes of TV-shows. Every chapter has its own storyline about the same characters, but eventually it leads up to something bigger. It's hard to help you with the info we got, I'm afraid.
why don't you post the ending paragraph of one chapter and the beginning one that follows, so we can get some idea of what you mean?
You might want to read some of George R. R. Martin's books. I think he links the otherwise separate chapters together very well.
Agreed - is it like a sitcom-esque thing, where each episode presents a different situation with the same characters and world (more or less), or is it entirely different characters with different issues related only themeatic means? Or are they a bunch of initially unrelated stories that somehow link up together at the end? I also have one story that follows the episode-esque format, somewhat. There is still the overarching character development - i.e., all of the "episodes" have my major characters develop somewhat towards the end - but otherwise the stories can somewhat stand on their own.