These days we have the advantage of installing flexible stainless steel liners to woodstove inserts and to oil furnaces.
Flexible stainless steel liner kit. I think it is important that only a poly brush be used for cleaning. A brush made of round or flat wire brush could rip the liner if it encounters an acute angle in the liner. Sometimes a liner is installed at an acute angle somewhere in the chimney flue. Poly brushes are much more forgiving than wire brushes.
round poly brush used by a chimney sweep.