I have an exception "of necessity" to what Magneticanomaly has posted. Namely, in some applications, the flat face pulley is often the 'driver', as when driving 'tight and loose' pulleys on the driven shaft. The driver pulley is 'double width' to allow the belt to be shifted to either the tight or loose pulley. As such, this driver pulley is machined without any crown. The crowning on the tight and loose pulleys causes the belt to run where it is required.
An extreme example of this would be the flat belt drives used on some of the old cylindrical grinding machines. The driver pulley was a long, straight cylinder, long enough to allow full travel of the machine parts. Another extreme case of this principal was in the original Colt firearms factory in Hartford, CT. The factory used line shaft drives for the machine tools, and made much of the line shafting in the form of long cylinders or 'drums'. This was to allow positioning machine tools wherever needed along the line shafting without having to mount individual pulleys.
Another thing to remember with leather belting: as noted leather belting will lengthen with humidity and will become permanently stretched if left under tension. In the old line shaft shops, it was common practice to 'take down the belts' before long weekends or holiday breaks. This was done by 'throwing off' the belts. With the lineshafting running, a hammer handle or smooth wrench handle was often used to walk the running belt off the pulleys. Once that was done, the more fastidious shops had heavy wire hooks in place near the line shaft pulleys. The belting was hung on these hooks to keep it off the oily lineshafting. Lineshafting invariably became oily from oil seeping out the ends of the lineshaft hanger bearings. There was either a cast iron trough below each hanger bearing, or an old coffee can hung on wire to catch the oil. However, some oil did make it out along the shafting and mixed with airborne dust to form a kind of sludge. If the belting laid in this sludge when run off the pulleys, it would soak up plenty of the oil. I worked in shops where we 'ran the belts off' on Fridays in the summer months due to humidity and potential for the belts to stretch and 'take a set'. Monday mornings, we had the job of 'putting up the belts'. This was done with the foreman standing guard at the motor starters for the lineshaft motors to prevent accidental starting. Using stepladders, we climbed up and got the belting started on the pulleys and then used a variety of maneuvers to roll the lineshafting to get the belting fully on the pulleys. Usually this meant one guy was on the large pulley at the belt from the drive motor, getting leverage on the spokes or making like a hamster on the inside of a treadmill. Despite this, the shop had a cart made up to deal with slipping flat belts. The cart was something knocked together eons before from old lumber. On it, there was a 'Clipper' belt cutting shear, which cut the ends of belting to about 6" nice and square. There was also a Clipper belt lacing machine and plenty of packs of hooks and rawhide pins. If a belt was too slack, the cart was rolled over and a piece was taken out of the belt. How much taken out was usually a matter of experience on the part of the machinists. On a long flat belt that had gone slack from a combination of time, wear and humidity, it was not uncommon to see a chunk 2 to 3" taken out.
The sticky black belt dressing used was "Kling surface" and came in the form of a stick. Have'nt seen any of it in ages, but remember using it on running belts. Rosin can also be applied to leather belts to increase the friction.
As for non-leather belts: Hanford Mills has many lineshafts and many belts driving a variety of woodworking machinery. It is an old, drafty mill building with the tailrace from a water wheel running openly thru the bottom of the mill, so humidity is always present. Hanford Mills uses rubber/canvas belting, and lacing hooks to join the ends. This belting holds up quite well and seems less susceptible to humidity and stretch than leather belting.