It can also increase firebox temperature by reducing heat loss through the pipe, without actually “crankin' up” the fire. Often the flue pipe damper can be used to control flue pipe temperature without making drastic changes to the fire itself. Of course, reducing “suck” will indirectly reduce the amount of incoming air… usually, that is. It does this by reducing the amount of “suck” the chimney can apply to the firebox.
The flue pipe damper doesn't directly affect incoming air… it limits the outgoing gasses (smoke and heat). It’s a balancing act and sort of a learning curve, what works for your set-up may not work the same with another… don’t be afraid to experiment a bit until you get a feel for what works when. Air coming in under the coal bed will cause it to burn hotter and faster than air washing over the top. For (one) example, if you’re burning wood that coals-up heavily, such as elm, hard maple, oak and such, you may find opening that a bit more and closing the top slightly will keep the depth of the coal bed under control. The ash door spinner draft is a “secondary” or supplementary air feed… you may, or may not need to use it depending on conditions. That top air is your “primary” air feed… you need it to a certain degree or your glass will eventually turn black. Depending on how the air travels through the furnace before actually entering the firebox, it may also be pre-heated to some degree.
The, clean, fresh air “washing” down over the glass insulates it from soot and creosote build-up. The main purpose for bringing air in the top is to “wash” the glass door and keep it clean. The Englander isn't designed as a secondary combustion furnace… that doesn't necessarily mean it can’t achieve it to at least some degree though.