I've bought at the store or at yard sales, or found in the trash or
inherited from an old guy several kinds of flux, but I've alsways
saved them for copper pipes, and relied on resin core solder to do
electronics and electrical.

Is this what you guys do?

Sometimes I have trouble getting the solder to spread out, even when
I've scraped the wire etc. with a knife and gotten it very shiny.

One case last week involved 20 gauge single strand wire that had a
white plastic covering and a black plastic covering over that, even
though there was no braid or anything (why two layers?)

Should I be using the flux in cases like this?

Are there any things I should know that aren't obvious among the
following:

Oatey No.5 solder paste, cleans, fluxes, in a round red can a half
inch high
Oatey No. 95 Lead Free Tinning Flux for use with any lead free solder,
in a green can the same size as the red can above.
Kester soldering paste, in a 2x2" square blue metal can about a half
inch high with rounded corners.
Kester All Purpose Soldering flux, liquid in a 4 oz white plastic
bottle.