Is cannibalism part of mainstream food-chain?
Cannibalism can be found across most animal groups. For some groups of organisms (e.g., spiders, fishes) cannibalism can be common within a single generation. Sometimes it will be between siblings, but more often with other members of their species.

As @heracho pointed out, from a network/food web/flow-diagram perspective, yes, cannibalism is repressed as a negative feedback loop on itself.

Evaluating the statement: "Food chains are found within the population of a species," I interpret is as, within species, there are subgroups that consume subgroups, that consume subgroups. You'd need at least 3 levels for it to be considered a chain (i.e., you don't have a chain with two species/a single link). Cannibalism would be a single link/two species, and not considered a chain. As to whether or not chains exist within a species, I suspect it is not common if it exists at all. If it did, I would guess it'd be found in a group like fishes where prey are often size dependent.