I have inserted a flowchart object using:
Object -> Symbol. I can not change the stroke width as I usually do from the
fill and stroke. Even when I try to make the stroke width to 0, it has not effect in that symbol. The problem is illustrated here:
Symbols behave much like clones, so their properties come from the original object. I'm assuming you don't want to edit the original, just this particular instance. Therefore, click your symbol once to select, then go to Edit / Clone / Unlink Clone (or Shift + Alt + D). That changes it to a regular Inkscape object with nodes, and you can change stroke width, colour etc.