Now we need to find out why the other solutions (vinegar with sugar, vinegar with icing sugar, vinegar with brown sugar, red bull with sugar etc and water with icing sugar and water with brown sugar) havent worked
Obviously something required for sugar crystal growth wasn't present. I can't really help much other than to offer some possibilities that I have no real knowledge of.
By adding vinegar, a weak acid, to the solution, you have changed the pH and increased the ion concentration of the solution. I'm not sure how this physically affects sugar crystal growth; however, it will change the surface tension of the solution, the solubility of sugar, the heat of vaporization, and other physical properties of the solution that may or may not affect sugar crystal growth. It may affect what wicks up the string.
You will have to look on the Red Bull container to see what it contains as I'm not familiar with its chemical composition.
1) Have you seen any evidence of anything precipitating out of solution and lying on the bottom? If there is a precipitate, then you might have a chemical reaction or a physical separation occuring instead of crystal growth.
2) Did you add an excess of sugar to these vinegar and Red Bull mixtures until you couldn't disolve any more? If you didn't, then you probably don't have a high enough sugar concentration for crystals to grow given the other chemical and physical properties.