Hi Vickb 17 UK.
I take it the thread that came with the kit is some sort of rope coloured or black cotton, like sewing thread, and if it's been roughly wound round a cardboard keep you'll have bends or kinks in it. If this is the case you'll have to carefully wash it without getting it tangled (easier said than done.) then hang it up to dry with some small weights to keep it straight. When dry and before using it run it through some bees wax, do not use ordinary candle wax as this doesn't work, this will stop the thread from fraying and becoming hairy, and make it easier to get a small amount of sag or loose tension. but you might find it better to replace the thread with some nylon or mono-filiment thread on a reel, just remember to not pull the thead off the top of the reel as then you'll put a twist in it, it should be pulled of with the reel rotating as on a sewing machine.
As Ratch said above, the rat-lines, those ladder type things that go from the decks to the crows nests shouldn't really have any slack, the same thing goes for the standing rigging that's the rigging that holds the mast up. The only rigging that had slack is the running rigging, that's the rigging that hold the sails, and the spars the sails are arrached to. if you use bees wax it should be possible to put a slight bend in the thread and it should hold that shape, just don't tension it too much.
Hope this helps and good luck and if it's an Airfix kit would love to see the results of your endevours.
Remember we do this for fun John the Pom.