The chimney may have a coating of creosote that is getting rain washed down the flue tile. What does it look like at the top of the chimney? Is the crown in good shape? Is there a cover over the flue tiles in the chimney?
Also, the stove pipe connecting to the flue thimble is upside down. The crimped ends point toward the stove flue collar.
Also, the stove pipe connecting to the flue thimble is upside down. The crimped ends point toward the stove flue collar.