How does the energy of a solar flare propagate? Does it radiate outward, spherically, or is it more directed? Is there some opening angle? Is it more complex than this?
 A: It is very complicated because a solar flare is a chaotic instability in the solar plasma.
A: Since the original definition of a solar flare only depended upon an increase in x-ray flux in a small spatial region on the sun1, the energy of a solar flare would then propagate in the form of electromagnetic radiation.
However, our current understanding would require that we include the beaming of ions and electrons by the processes ultimately responsible for all of this (i.e., magnetic reconnection) that are sent both into the interplanetary medium and toward the surface of the sun, i.e., kinetic energy flux.  Most of the electron energy kept near the sun is converted to x-rays through thin and thick target bremsstrahlung radiation.  The trapped accelerated ions are more difficult to detect as the conversion to electromagnetic radiation is not as efficient and these tend to cause nuclear reactions producing gamma rays.
Footnotes 


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*Well, the first observations were of only white light flares, which tend to be the strongest flares for numerous reasons.

