Do I need to disassemble the tap head and how do I flush the lines?

Please leave the toolbox exactly where it is. The solid tap head is a permanently attached unit and does not need to be disassembled for cleaning. To prevent sweet syrup residue from clogging the lines, we have a brilliant trick straight from our development kitchen:

Simply rinse clean, warm water through the openings. Now, gently press the small, spring-loaded plunger at the front center of the tap connector, and the internal valve will magically open. The rinse water rushes unimpeded through the entire channel, taking every last drop of your drink. It doesn't get any faster or cleaner than that.