1/350 anchor chain and rigging

Another trick for coloring invisible thread, or stretched sprue if you use that for rigging (my personal choice due to the cost - none) is to use a Sharpie permanent marker to color the thread before installing it. Sharpies come in black and a range of browns to get a more correct color for the signal flag halyards and the like. As mentioned use CA glue to attach and then make the shiny spots go away with a small dab of flat clear paint to finish it off.

As far as the anchor chain, if you came up dry at Model Expo, try Bluejacket ship crafters online. As for the thread, go to a fabric store and get "invisible thread" It comes in a grayish color, is monofilament and shrinks in the presence of heat such as a smouldering match. I've used it on many ship and aircraft models with much success. The match insures it will always be tight. Later, I paint it with thinned black on a brush that I simply run the thread between the hairs and it coats with one stroke. Don't glue it with solvent thread as it will dissolve. Use CA in your favorite consistency. It also glues to itself very nicely for those aerials that have a lead coming from the middle of the line.

Good luck