There are a couple of ways to do flashing. Most common is a two part deal. Ther is a base flashing or step flashing that is an "L" shaped piece intertwined with the shingles on every course and hsaving a leg extend up the chimney. This leg is facing uphill to catch water and cahnnel it into the house so it is covered by the second part, which is called the counterflashing, set into the masonry. Normally, in an olkder roof as youdescribe, the counterflashing is left in the chimney and the base falshing is replaced with the shingles.

i cannot tell from your wording but it seems as if there was no counter flashing yo start with

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