I'm no expert on woodstoves, but I can say this from
experience.....
We hooked up our first woodstove to an existing chimney, a block chimney lined in flue pipe. The stove pipe made a 90 degree turn to run horizontal then another 90 degree turn to run vertical into the chimney. The draw was terrible, so bad that we couldn't use the stove.
A woodstove guy came out for a look. He told us that the two 90 degrees turns were part of the problem. The old chimney was also part of the problem because the diameter was greater than the diameter of the stove outlet, plus it was masonry (which is cold are takes longer to heat up for a good draw).
We modified the stove pipe and removed the lower section of the chimney in order to make a straight run vertically into the chimney. We didn't have the money to do anything else at the time. It got us through that first year. Then we opted for a double wall woodstove chimney with a straight run, used it just fine for 19 years until we sold the house.