Can electricity flow through vacuum? People say yes, and give a wonderful example of vacuum tubes, CRTs. But can we really say that vacuum (..as in space)  is a good conductor of electricity in a very basic sense?
 A: No, in the very basic sense it is not a good conductor, because very high voltages are required to shoot them through. But yes it still is a conductor, because it allows the flow of current.
Compare this to a diode, which similarly only allows current (in the same very basic sense) to flow if a certain voltage is applied.
Such non linear behaviour exceeds anything one would describe as basic, but if the basic sense of a conductor is that it allows current to flow, then it is a conductor indeed.
A: Electricity is a flow of electrons. Electrons can flow across a vacuum. The problem with doing this over a long range is that you need a force to get the electrons to travel across the vacuum.
In a CRT the cathode is heated, which gives the electrons the energy they need to escape the cathode. A large electric field then accelerates the free electrons across the vacuum and onto a target (screen). In this case, other fields are also used to steer the beam to get an optimal picture.
If you have a different system - imagine an anode and a cathode in a vacuum seperated by a small distance - with no deliberate heating taking place - then the potential difference (ie potential energy or voltage) between the two electrodes must be large eneough that the electrons can "leap" between them. They need to leap because the vacuum is a perfect insulator and so there is no medium in which they can flow (like through a metal conductor) so they must aquire all of the energy necessary to cover the distance before they can escape the cathode. Larger gap to be traversed implies larger potential difference required to get the electrons to make the leap.
Hope that helps.
A: 
But can we really say that vacuum (..as in space) is a good conductor of electricity in a very basic sense?

No, because vacuum is not a material object. The word conductor was meant for material bodies. It is not usually used to describe vacuum, because vacuum is not merely a different body from metal or dielectric, but it is a different concept - a lack of matter.
(Language note: it is possible to let charges pass through it with no resistance, but I would not call it conductor just because of that. Conducting is associated with influence of the conductor on the motion of the conductee - directing the motion - which vacuum does not have.)
A: The conductivity of the vacuum is not a very trivial issue. In fact, depending on how you look at it, it behaves in two different ways.
Firstly, there is no retarding force on any charged particle with constant velocity in vacuum. To this extent, no extra work is required in maintaining a constant current through any surface in vacuum.
In stark contrast however, is the presence of free charges in conductors. Normally, when an electric field $\mathbf{E}$ is applied across a conductor, we get a current density due to the 'internal' charge flow, given by:
$$\mathbf{J} = \sigma\mathbf{E}$$
where $\sigma$ is the conductivity. Clearly, $\sigma = 0$ in a vacuum - electric fields do not spontaneously cause currents to flow. Thus, in this sense, the vacuum is not a conductor at all. Even everyday insulators have low but non-zero values of $\sigma$.
Thus, the resistance of the vacuum is in fact, infinite, as long as we define resistance in terms of the response of the charge carriers of a material. In this sense, we might say that it is an insulator - there are no charge carriers.
A: To make things even more confusing, there is a sense in which we could assign the vacuum a "resistance" of 377 ohms: https://en.wikipedia.org/wiki/Impedance_of_free_space
A: Conduction of Electricity in Solutions, Gases and Vacuum
https://youtu.be/7q8f-QJlpsA
What should be the definition of "Electricity"?
http://www.ivorcatt.org/99mcattq.jpg
http://www.ivorcatt.co.uk/97rdeat4.htm
http://www.ivorcatt.co.uk/x18j100.pdf
Ivor Catt states here that electric charges do not "exist".
http://www.ivorcatt.co.uk/x0620.htm

*

*"In the same way as the slope of a hill does not exist, having no materiality, although the hill itself exists, being made up of physical material, so electric charge and electric current become merely the results of mathematical manipulation of the edge of a field (or more accurately of an ExH Energy Current)."


*“Although a cloud cannot exist without edges, the edges of a cloud do not exist. They have no width, volume or materiality. However, the edges of a cloud can be drawn. Their shapes can be manipulated graphically and mathematically. The same is true of the so-called ‘electric current.’”
Also. please do see this Electron mass experiment
on Youtube. This is a transcription: https://imgur.com/a/luE4CC9
A: Summary: (?) A vacuum is the absence of atmosphere and is a neutral force--offering neither resistance nor conduciveness to proton/electron flow. The state of "vacuum" does not compare with the state of "space". Any/all space is a physical measure of distance and can be overcome by the optimal difference of potential.
A: I think the problematic part of the question is the word "electricity", which is not a useful modern description of phenomena surrounding electric charge and electromagnetic fields. Charge is a phenomenon that is invariably coupled to matter. Electromagnetic fields are a phenomenon of the vacuum. Both are connected in a very deep way trough quantum mechanics. Ultimately both matter and electromagnetic radiation are different expressions of the same quantum field that permeates all of the vacuum, but there is virtually no way to express that connection properly on the level of macroscopic "electricity". What the vacuum does is to allow matter to pass trough it. Matter can carry charge, moving charge is "electricity", but it's ultimately not the charge that transports energy, but it's the electromagnetic field that is linked to it, and that field can transport energy without the need of charges, at all, but the latter is usually not called "electricity", which makes the word "electricity" of limited use to describe proper electrodynamics.
