Plozen, Welcome to Physics Forums! This is a place where real scientists, engineers, and other highly experienced people contribute to your understanding of science, technology, engineering, and mathematics.
I will give you an example of how "current flow" was taught by the US Navy Electronics School fifty years ago. It worked quite well in those days, but be advised, this is only part of the answer to your question.
The simplest vacuum tube amplifier is a triode, meaning it has three electrodes: cathode, anode (plate), and control grid. The cathode was most negative and had a heating element that glowed red-hot. This caused electrons to "boil off" and be attracted by the anode, which was at a high positive voltage...typically +250 volts. The control grid was a screen between the anode and cathode which controlled the flow of electrons. This triode could amplify a small signal placed on the control grid. We said: "Current flows from the cathode to the anode". Our rule was "current flows from negative to positive", which made sense to us, since we knew electrons had a negative charge. We used the terms "current flow" and "electron flow" interchangeably.
Now, that is only one part of your answer. I defer to other (younger) contributers here to explain the rest of the story!