Normally you need to be careful when mixing flues from different-fuel-sources;
heating-oil-fired boilers & furnaces are normally not-compatible with wood-burning-fireplaces
(incompatible-deposits can more readily start a chimney-fire).
A multi-fuel chimney or flue either:
has separate-flues for different-fuels
or is made of materials which lessen the hazards and/or risks of chimney-fires.