A.John Carroll, a builder and mason living in Durham, N.C., responds: As late as the mid-19th century, bricks were stacked and fired in temporary, site-built kilns, then sorted later. The ones closest to the fire — "clinker" bricks — were very hard, but often distorted and sometimes fused together. They were considered ugly and were mostly used where they wouldn't be seen — though nowadays they are valued for their dark, uneven color and irregular shape. "Face" bricks were located a little farther away from the fire, so they were hard and dense but retained their rectangular shape. These bricks were reserved for the exterior face of outside walls. The bricks farthest from the fire — "fill" bricks — were used on the inside of exterior walls and for partitions inside buildings.
In general, fill bricks are larger than face bricks and pinkish-orange or salmon in color. They have a softer surface than face bricks; when you strike them with a hammer, you'll hear a thud rather than the ping you would hear when hitting harder, denser face bricks. The biggest problem with fill bricks is that they are porous, so they soak up water and deteriorate rapidly when exposed to freeze/thaw cycles (see photo, below left).
Even if you can accurately distinguish between the face and fill bricks, though, I wouldn't recommend using either kind for an exterior chimney. Unlike exterior walls, which often have protective eaves and rakes to protect them, a chimney — at least the part above the roofline — is completely exposed to the weather. Here you should use modern face bricks. There are traditional styles available, yet they're manufactured under controlled conditions and laboratory-tested for water absorption. They're also much more consistent in quality. Save the old bricks for projects inside the building.
Be sure to match the mortar to the bricks. As a rule, mortar should never be stronger than the masonry units. If it is, any small stress on the structure will show up in the form of cracks and spalling in the bricks. Avoid modern masonry cement mortars, which are too hard, and use Portland cement and lime mortars instead (in most cases, you'll need to go to a masonry supply house to get the hydrated lime). To lay soft fill bricks inside a building, use Type O; if you're intent on using salvaged face bricks in an exterior application, use Type N.