A few years ago I installed an 8 inch chimney in my shop and it has a leak which I thought was coming from the boot I installed but it appears that it is coming from inside the pipe, not sure how it could possibly get into the pipe.
rain will get into anything, it follows the path of least resistance and driving rain especially so. How big of a leak? Without seeing it or how long of a run it is, it is possible it's coming in from the top and running all the way down the stack.
It has the same kind of rain cap I have been using for over 40 years and never have I had water coming down inside the pipe before. The leak is significant especially with all the rain we have had this year. Once it dries out I will try and get a look at it but not sure what could be the problem.
Mine has leaked once when it was brandy new, down the outside of the pipe and into the house visible on the pipe in the room, but never again. I never found a possible source for it. Getting into the attic wasn't worth cutting the ceiling open for. It may have been an ice build up that likely won't happen again . My sister had a leak after a Northeaster and I retrieved her cap from the neighbor's back yard. I also put a cap on her oil burner chimney. I don't think it ever had one.
Assuming we are talking about Double Wall insulated pipe, since you have a Boot on the roof, I would believe it would have to be rain blown into the cap and into the pipe. If it is Single wall pipe, it needs to be stainless steel, if you have galvanized, it could have holes in the pipe.
Slip lock double/triple wall? did someone twist it and it lost it's locking seal? If it's coming from inside the pipe and it's double wall, there is only 1 of two ways I know it could be leaking inside the pipe. The cap or the seal and the boot isn't sealed allowing rain to go down the outside pipe till it hits a open seam. If single wall, what double-d said.
People have had water leak into the exterior vertical seam on class a double wall. The fix was a finger of clear silicone run up the seam on the outside. More likely is the goody little umbrella looking storm collar right above the boot, gotta seal that with silicone too. What kind of roof?
I had a small leak along my metal chimney in the garage. It would only appear during heavy rains. I put a bead of silicone around the rim of the storm collar and the problem never recurred. I had used gutter seal but that stuff gets hard and brittle; breaks off and then you have a leak.
It's been raining sideways at times here recently... I would not be surprised if I have some on top of the baffle.