As depicted on the Zhentarim banner, Flying Snakes are commonly used by Zhentarim agents to communicate messages between other faction members. They would also use standard methods available to any mercenary company: private couriers, sending stones, or Animal Messenger. The faction often deals in illegal goods (slaves, poisons, drugs) and would be able to offer support with smuggling, buying, and selling such wares, as well as thievery, assassination, and other spy work.
As an example of using this for an adventure, a player could rely on Zhentarim contacts to locate recently stolen goods, track down rival thieves or assassins, or assist with smuggling operations. Some of these might be offered on a quid pro quo basis.
The faction could also be used to give missions to the players if a smuggling route has been taken over by competition, an item needs to be stolen, a person needs to be assassinated, or some goods need to be taken somewhere safely.