It's been a while since I had to make a flowchart. I made quite a few in my Corporate days. Some I did in Corel Draw, others in Microsoft Powerpoint. But the process was always ugly and required a lot of work.
Well no more! There a FREE online flowchart program online called Lovely Charts. I used it to diagram the convoluted system I had to develop to get internet and VOIP phone working in my home. It takes no time to pick up how the system works and it has a lot of pre-made objects (like networking icons). I only wish they had more objects to work with, but hey, it's free.
And if you're curious what the network looks like that makes Bag End function you can see my kick-ass diagram here (click to embiggen):