Ceiling wet at corner of chimney
98% of small leaks are water getting into the flashing area between the chimney and the flashing or the flashing and the shingles.  

The flashing sealant you have should work fine - although you need to make sure for a caulking type sealant that this is applied liberally and squeezed into the gaps.  I often use FlexSeal for smaller leaks because of its expanding properties.  

If you post a picture of your chimney I can highlight where you need to seal.