the chimney is ok as-is. However, you DO need to stop the reason for the spalling and flaking brick or it will get to the point where the top of the chimney from the attic floor up needs to be rebuilt. The reason the brick is spalling etc. is because of excessive amounts of moisture - either leaking between the chimney and the flashing or through poor mortar joints and the brick itself above the roofline. have someone take a look at the flashing and replace/repair and see if the chimney needs to be re-pointed as well. it wouldn't be a bad idea to clean the stack above the roofline and coat the chimney with a good BREATHABLE sealer. In your area AH harris carries a good product for your chimney: http://www.ahharris.com/Data%20Sheets/HARRIS%20Kurseal%20309%20Emulsion.pdf MOST IMPORTANTLY check to see if the flashing needs to be repaired, then be sure the chimney above the roofline is in good shape or is repointed before applying a sealer.

Good advice from berlin about flashing and water issues. I would, however, have someone check the interior of the chimney. Chimneys of this vintage often were built with no lining at all. If yours was lined with tile, it's a good idea to see what shape it's in.

If the chimney is connected to a fireplace or other wood burning appliance, a liner is really a necessity. If it's connected to only a furnace or boiler, a good liner is also needed in light of the deteriorating mortar.

A stainless steel liner can be installed. Even better for old chimneys,IMO, is a poured in place liner. This will fill in any cracks and strengthen the entire chimney from bottom to top. Supaflu is one brand of poured in place liner. www.supaflu.com

Thanks so much berlin. Thank you mainegrower. Your knowledge and advice is much appreciated!