I have giving this topic of yours great thought.
Perhaps fine fishing line could be used on your model ship,because that stuff is made in the same way as is larger rope,so you won`t have to make yours out of cotton or fine wire perhaps stripped out of a length of electric cable. Years ago I made a hot air balloon,and made the basket ,the rigging and,the net over the balloon using fishing line.
On You Tube plenty of stuff on how to make rope for ships rigging,and how to rig sails and such. It is going to be very fiddly work, but then you knew that when you bought it.
The sails out of kitchen foil perhaps. Fine cotton linen fabric.
Or the sails out of ordinary A4 size paper,or brown or green parcel wrapping paper
For my narrow boats I made the canvas coverings out of paper.
Try doing a sample first.
Screw up paper into a ball.Unscrew it and screw it up again but in a different direction and repeat again and again,this does two things it makes the paper very soft and not stiff like before.It also help give the natural look of canvas. Using a water based colour wash paint dab and let it dry,this soaks into each and every tiny crease, giving hopefully the look you require. When dry add more differing colour washes here and there.Then let it dry and then cut out your sails. You can use the plastic sail`s that came with the kit as ten plates for each sail if you like.Stick your rope,( perhapes fishing line or cotton twin) ,onto them then try and form your sails how you wish them to look laying them on something curved might help,and stiffen each sail up using a cheap hair spray, ( 35p ) I have never used spray polish to do this job,so I don`t know if that would work.
You will need to spray it a couple of times on each side. If your paint is water based on your sail`s this will not cause ruin to it. If this is of help to you,and you wish to try it,you might even find a better way of doing it. I find people often underestimate the use of paper in modelling projects. It is the cheapest of things on this planet and If it does the job ,it`s all well and good.
I must add this, This is not a wind up! And also not all my quirky ideas work out.
Picture in public domain.)
Below the famous picture known the world over,and you can see lots of rigging and flags on Henry VIII Flag Ship.
The Mary Rose : 20 heavy guns made of bronze weighing up to two and a half tons each, and 60 light guns a complement of some 500 men. There were 30 gunners that were in charge of certain guns and gun crews that managed them.
By the way that ships hull is looking very impressive in need. BB