How much clearance do I need above a floor vent?
You don't need nearly 4". You can basically take the width and height of the gap on three, or even four sides of the floor vent into consideration, depending on how much of the undershelf area is open to the room. The air that comes through the grate can distribute to the sides as well as the front, and eventually make its way out from under the shelf. 

Air movement looks something like this (assuming that that shelving is tight to the wall):

|               *               *               |
|               * ############# *               |
|               * ############# *               |
|               *****************               | 
|_______________________________________________|

| : shelf perimeter
* : outflow area perimeter
# : vent area


The math looks like this:

original vent area (disregarding the grille) [av]: 40 square inches
distance between the vent and the wall (hypothetical) [dv]: 2"
outflow area perimeter length [op]: 2 * (4 + dv) + 10 = 22

required height: av / op ≈ 1.8 (1-13/16) inches


With that in mind, an inch may be enough if the vent is further from the wall than I've assumed, or if the rear of the shelf is open to the room (up behind the shelving unit). It would be different if it was a return, where vacuum pressure is low, where resistance due to airflow path bends is a more significant factor. 

If the shelving unit has side panels that reach to the floor, you can simply calculate the entire frontal area of the void below the bottom shelf. If it's over 40 square inches, you're probably golden. The exception would be if the vent is very close to the wall, wherein you'd go back to the math above.