Do NOT use a holesaw, leetle 3-4" holes may be fine for attic soffits but they are WOEFULLY INADEQUATE for chicken coops (which have higher ventilation requirements than a house, btw).
What tool to use to cut large vents depends on what exactly you're doing. If you will only be cutting between studs, drill big holes at each corner of the prospective rectangle and then use a power jigsaw, reciprocating saw, or keyhole saw (as per personal taste) to 'connect the dots' to cut out the rectangle. I recommend cutting the holes from INSIDE the coop, that way you KNOW you are not going to run into studs! You will have to sand the snaggly bits off the opening no matter which direction you drill, and can do the *saw* cuts from outside if you want.
If you want your vents to cross studs (without severing them obviously
, just having the studs exposed in the vent) then either remove the siding, cut it to size and replace it, or if it is wood siding (sorry, your links were not behaving well for me on slow dialup so I have not viewed the actual shed in question) you can set your circular saw blade VERY VERY ACCURATELY to the depth of the siding and cut across, then use hadn tools and some swear words to finish breaking the panel of siding free.
Honestly, if you live in Florida, you probably want most of at least one wall to be all-mesh, so just removing large expanses of siding altogether would be by far the easiest way to do it! (Replace with securely affixed hardwarecloth)
Good luck, have fun,
Pat