How much air does my preamp need?

According to the user manual:

"Allow at least 6 inches (15.24cm) above the top, 2
inches (5.08cm) below the bottom and 1 inch (2.54cm)
on each side of the Tube Preamplifier, so that airflow
is not obstructed. Allow 19-1/2 inches (49.53cm) depth
behind the front panel.

It's hard not to go with the manufacturers recommendation but a preamp doesn't make a lot of heat so I would be OK with an inch on top and open everywhere else. Way more clearance if the back is on the shelf. 

Not enough room your looking for trouble with that setup.

Heat is not a friend of any electronics equipment 

Do follow the manufacturers directions.   They didn't ask for a lot of space because it looks cool.   They know the more space they specify the harder it will be to include their product in some setups.  More ventilation is always better than less, so the manufacturers recommendations are a starting point but then there is not a critical need to exceed it either.  The critical need is to meet the requirements.