Fire in the hearth will deposit soot and tar in the chimney to a certain extent depending on the fuel and the temperature of burning. In general, the cooler the fire is, the more soot and tar is deposited - the hotter, the less soot and tar.
As to potato peelings which have been dried, I have no specific reference as to the latent energy of combustion, I'll have to take your word for it that they burn fast and hot.
There is a tipping point at which the chimney starts to clean itself - this is called a chimney fire. This may result in the catastrophic failure of the house structure, as small gaps in the masonry next to surrounding timbers promote their combustion, or the masonry becoming so hot; that the surrounding wooden structure will start to burn. This is not always the case, but it's a judgement call that would need to be made by a suitably qualified professional.
There are some damage limitation tips: here.
The only effective and safe way to clean a chimney is with a Sweep's Brush and Rods. (From a UK Government Agency)
As to further references and reading, this document is highly detailed and comprehensive: Here.