Relation between energy flow and electronegativity

In general materials are more conductive if they are made of same element so elements with same electronegativity are connected but non-conductive if electron current would have to switch from one element to other many times on the way. Also if they conduct electricity then they are probably good conductors of heat like metals. There are some exceptions as diamonds don't conduct electricity well (about 100 times better than glass) while being fast at conducing heat but this may be due to bit chaotic looking crystal structure (lack of straight pathways to flow to). Other pure carbon materials like graphite and nanotubes are good conductors and their simple structure allows more parallel flow of electrons.
Electrons are attracted to more electronegative elements and that could have predictable effect on electrical conductivity.

For example insulating quartz is made of silicon and oxygen connected one after other. If electron flows through it then it is bit attracted to every oxygen atom on the way unlike to silicon atoms around oxygen which lose electrons easily. Electrons could flow relatively easily from silicon to oxygen but not from that oxygen to any neighboring silicon atom so in large scale glass is about as conductive as air or vacuum. That may be the main reason why pure silicon is about billion to trillion times more conductive than glass.

Above are 4 examples of transparent conductive polymers which may be used in transmitting current through transparent materials like touch-screens. They also tend to have one type of element in main chain but there may be other elements in main chain like sulfur which has about 1% higher electronegativity than carbon. Possible that they are transparent while metals are reflective is due to only guiding energy in straight line not in every direction like in piece of metal. If light is polarized parallel to this chain it may more likely absorb but at same time allow light to pass if it is polarized in any other direction.
Many non-conductive polymers have oxygen atoms in main chain like polyester which can easily collect static electricity but there are several non-conductive polymers which don't have anything in main chain beside usual carbon and hydrogen.
Other special feature that these conductive polymers have is lack of charged parts next to main chain.

For example above structure is of non-conductive plexiglass. While main chain is carbon it has side chain that has oxygen atoms which could probably pull to the side any electrons that would move through main chain. Nylon has main chain with carbon and nitrogen but the the side it too has oxygen atoms that may interfere with its conductivity.  

(Diode in above image) Electronegativity is in some ways used in electronics to create predictably routed flow of electrons by doping silicon with some element from group next to silicon. Adding aluminum (or other III A group element) would make it more positive (p-doped) and sulfur or arsenic from more electronegative 5th group can make it more negative (n-doped). 1 n-doped and 1 n-doped material connected together can create one way current in diodes. While electrons easily flow from negative area to more positive area, they may not flow at all in opposite direction or only if some high voltage pushed it against easy direction. Such setup is used in rectifiers to convert alternating current to direct current allowing only one way direction flow. Similar setup was used in cat whisker detectors in early radios that turned alternating current produced by absorbed radio waves in antenna into one way electricity. 
LEDs use such diodes to create light or electricity. If electrons flowing in one direction get at least 1,2 electron volts of energy then they will start to glow. Same LED could create current if it was exposed to energetic enough photons that could get electrons moving (most likely only in one direction due to larger resistance in other direction).

Electrical conductivity is close to thermal conductivity as electrons carry energy/heat about as fast as wires could carry electricity. In this regard electronegativity could be used to predict how well and in what direction will materials carry energy/electricity/heat with the precision close to size of atoms involved. This precision could potentially be further increased by using magnetic fields to align atomic nuclei (and their electron movements) with outside magnetic fields or by smaller magnetic field produced by local groups of atoms. Cooling near absolute zero may further help to keep precision of interactions between atoms.