Flashing gives more warning than almost any chimney component, if you check from both sides. Outside shows the cause; inside shows the consequence. Either alone is worth a call; both together is a certainty.
Outside: what binoculars can catch
Inside: the rain-pattern test
The flashing-leak signature is timing: stains that appear, darken, or drip during or just after rain, on the ceiling within a few feet of the chimney, or down the chimney breast wall. Contrast with crown-route water, which moves slowly through masonry and shows up delayed and diffuse. Sharp rain-correlation = flashing until proven otherwise, the full differential here.
The attic look (five minutes, definitive)
Flashlight, next rainy day: find where the chimney passes through. Water tracks, dark staining on the chimney’s exterior face, wet insulation at its base, or active drips at the roof-penetration line are the closest thing to a confession this leak will ever give you. Photograph what you see, it calibrates our visit and starts your insurance file if a storm caused it.