From what we know of back when a bucket brigades were the fire fighting method of choice,
Before the mid-1800s, the most common way of fighting fires in the nations cities and towns was the bucket brigade, made up of volunteers. When a fire was spotted, the cry of "throw out your buckets" would be sounded, and a bucket brigade would be formed, two lines of people stretching from the town well to the fire to deliver as much as sixty gallons of water per minute.
A colonial fire bucket holds approximately 3 gallons of water and weighs 25 pounds when filled. A human bucket brigade working at top speed would struggle to deliver 100 gallons of water per minute.
At the same time, I would say that the people back then had practice doing this, and most people today would not. Over longer distances I would expect the speed to decrease, simply because there are more moving parts to slow it down and you can only go as fast as the slowest person.
On other thing, I was part of moving several hundred pounds of copier paper down one flight of stairs by passing them from person to person, and the other big limiter is the speed of the people on the ends of the chain.