The chimes cap may be leaking, but the more likely cause is the flashing looks bad.  This type of flashing is called angle flashing and can leak unless adequately sealed during construction.

The angle flashing here makes it easier for this roof to leak.  The chimney and the wall need to be reflashed to fix these leaks with step flashing.

This repair option is to reflash bot locations with new shingles and metal.

This pipe boot is leaking into the bathroom.