The best sleeving material to use is the outer cover of some 2mm rope. You can buy some short lengths in the colours you want to colour code your sleeving. Simply cut it to length and pull the core out.
When you melt the ends push the tip of a pen or pencil inside the sleeving a little to flare it out so it opens up nicely. Don't melt too much or it will be too thick.
Grab an old guitar string, fold it in half and push it through the sleeving. Put the kite line through the string and start to pull it into the sleeving. Massage the end of the sleeving as you pull the folded end of the string into it.
Once you get the end of the line inside the sleeving push the sleeving down onto the line so it bunches up then pull the end of the sleeving down onto the line. Repeat this a few times and you will have the sleeving down over the line.
You don't have to use a lot of force. It's all about pushing the slack in the fibres around to make space for the line. Think of a big snake swallowing a small child and you'll get the idea.