The source and sink phenomenological description of charge - how realistic is it?
It isn't realistic at all. To be perfectly honest it's totally misleading.
I've heard over and over an electron described as a source of the electric field, but that is a misleading term.
Yes it is, because like Timaeus said, it's the electromagnetic field. See Minkowski talking about it in Space and Time:
"In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect".
Note how he said the field? It's one field and two forces. The electron doesn't have an electric field or a magnetic field, it has an electromagnetic field. So depictions like this one in Andrew Duffy's Physics 106 are misleading:
What's gone wrong is that there's this confusion between field and force. That's why you can read "lines of force are also called field lines". Electromagnetic field interactions result in linear "electric" force and/or rotational "magnetic" force. When we only see linear force we talk of an electric field, when we only see rotational force we talk of a magnetic field. Then when you make allowance for this error, the source-and-sink description is still wrong. Look at the directions of the arrowheads, and note that two electrons repel, two positron repel, and an electron and positron attract. There is no way those arrowheads "work" for that.
Source makes one thing of a tap, with a constant flow of something coming out of it. This is clearly not the case for an electron.
Clearly. Nor is it true for a positron.
I am trying to ascertain the validity of the following statement: A charge for e.g. an electron is a perpetual emitter of an electromagnetic potential flow [in the form of polarised virtual particle pairs popping into and out of existence] and is therefore a permanent creator, or rather a consistent initiator of a virtual flow of energy.
It's nonsense I'm afraid.
This intuitively sounds wrong to me, I think the author is taking the mathematical concept of virtual particles too far.
Agreed. When the electron and the proton attract one another they "exchange field" such that the hydrogen atom doesn't have much of a field left. This is the reality that underlies virtual particle exchange.