My gut reaction is that this installation would totally depend on wind at the site being minimal. If the sail is stowed every night after use, I'm sure this would be fine.
However, if you expect to leave it up through arbitrary winds, then my sense is 99% of the load on the 4x4's will be in shear - the wind trying to snap the 4x4s off sideways or tear/shear the bottom mount attachment. That is not something you can ask of 4x4 dimensional lumber particularly of Home Depot's offered grades. I see two ways to counter that.
First is a significant network of guy wires - connecting the tops of the poles to each other and to the house, then also diagonals on each axis to the ground. Internal guying within the house would also help, so wind and guy-wire strain doesn't just pull the wall over. (that can happen). Properly done, this will transfer all shear forces to the guy wires, and place the poles entirely in compression. Downside is you'll be tripping over guy wires all over the place.
Second is much more substantial poles, as one shade-sail site recommends:
We recommend the use of a minimum of 4 inch, schedule 40 steel pipe or a minimum of 6x6 inch wood treated for outdoors. Posts sizes are determinied by the size of the sail or sails attached to it, what sides they are attached and the height they are attached. Your local timber supplier or pipe fabricatore can assist you in your sizing. Post lengths should be taken into account the proposed height of your sail plus the depth of your footings. Footing depth should be 1/2 the length of the exposed pole. For example, if your post height is to be 10 feet, you would use a 15 foot long post with a footing depth of 5 feet in the ground.
You want to attach it to the concrete slab, but unless the slab has been reinforced for that purpose, I would not count on that.
Note that on your own sail's product page, the manufacturer shows smaller sails than yours being held up by very stout steel I-beams of at least 4" x 4" and at least 3/8" web. So clearly wind is a factor they take very seriously. You should too.
Steel I-beams can be had from any local steel distributor.
