I'm the one who made the stroller sleeve. I have 3 of them now, b/c I have several strollers, so they don't all fit universally. BTW, I recommend removing the hood of the stroller and putting it in your checked bag for the flight; hoods are bulky and easily damaged.
I make the sleeves out of bright ripstop nylon, actually; it's lighter than canvas and smaller to fold down flat, and it also repels water, which helps keep your upholstery dry if it is raining when the stroller is being moved into the hold. (The bright color makes it more visible to handlers who are bringing them up from the hold.) The inside of the hold *is* greasy, and the odds are that some of that grease will end up on your stroller; my stroller sleeves have some interesting grease smears on them. To use a sleeve, you fold the stroller in the gate area, put the sleeve around it, then drag it down the jetway and leave it with the others.
Making one of these is really simple, and depending on the shape of your folded stroller and the width of the fabric you buy, may not require any actual sewing, though a sewn sleeve is likely to be more durable than one that is done w/ fabric cement. Once the measurement is done and the materials are at hand, I can make one in about 30 minutes.
To measure, fold and secure the stroller with everything removed the way it would be for checking, then take a measuring tape and measure around it. In all cases, exclude the wheels and handles from the area being measured, unless it would be impossible to cover the upholstery and still exclude the wheels.
For an umbrella-fold: measure the width around the tube at the widest point (usually the upper set of wheels), then add 10 inches for overlap. Next, measure from the top of the lowest wheel to the bottom of the handles, and add 6 inches, that is the length you need. Make a one-inch overlap on each edge, you can sew this down or glue it w/ fabric cement, whatever you are comfortable with.
For a square-fold: measure from the top of the upholstery (putting the tape UNDER the handle) then down around the axle and back up to where you started. Make sure you do the measure OVER the thickest part of the upholstery, not along the side where it is thinnest. Add 10 inches for overlap. That is your length. Next, measure around the folded stroller at the widest point, which is often where the lap bar sticks out (if you won't be removing it, of course), add 6 inches, that is your width. Again, one-inch hem all around to prevent raveling.
Fasten the sleeve with patches of velcro spaced at about 3-4 inch intervals along the edges inside the 10 inch overlap. You will need to put the sleeve on the folded stroller to mark the placement of the velcro. Buy the widest velcro you can find, that gives you some adjustability. You can use one continuous length of velcro for the fastening edge, but I find this is less forgiving when trying to secure the sleeve, as you have to line it up and keep it straight.
Extra touches: For an umbrella-fold, you may wish to sew on elastic on the narrow sides (stretching as you sew it); it makes a neater finish around the bottom near the wheels, especially. For the square-fold, you might want to add an extra flap of fabric on the side edges that will secure down w/ more velcro. Lastly, you may wish to paint on your last name and some note like "Baby buggy; deliver to gate."
One other tip about these: If you are using a satchel to transport carseats to the gate, you can stash it inside the stroller sleeve for the flight; I just fold mine around the stroller frame and then put on the sleeve over the whole thing. It pads the stroller a little bit that way, too.