First, I have provided some background on these phenomena at: https://astronomy.stackexchange.com/a/16786/13663
Solar flares and coronal mass ejections (CMEs) are not the same phenomena.
I am aware that radiation from these solar events does not travel directly outward from the direction of the sun but follows magnetic lines of force and may be subject to eddies and other other effects that modify the direction of travel.
To what are you referring here? The only things that follows the magnetic field are charged particles. CMEs are huge blobs of plasma (i.e., ionized gas) that erupt from the sun and carry with them large deviations in the magnetic field. Both solar flares and CMEs can generate what are called solar energetic particle (SEP) events. CMEs can also generate something called an energetic storm particle (ESP) event. The distinction is the latter is an in situ inhancement of energetic particles that were generated by the shock ahead of the CME. The former can be generated near the Sun.
Solar flares are primarily distinguished by their localized enhancement of UV and x-ray light, neither of which cares about the magnetic field. Electromagnetic radiation propagates through space in the direction it was emitted and only really curves under extreme conditions (e.g., huge gravitational fields or extreme electromagnetic fields like those near a pulsar).
What does the graph of average radiation intensity v radial distribution look like for a point in deep space (radiation intensity v degrees bearing from the line of maximum intensity) for a passing solar flare or CME?
This depends upon what you mean by radiation. If you are asking about charged particles, then it also depends upon the event. Some CMEs "sweep up" and energize particles as they propagate so the intensity levels can actually increase with radial distance from the Sun out to varying distances (depending on CME strength etc.) then it will begin to decrease. So the answer is that it's very complicated and it depends upon the specific event. However, inside Mercury's orbit, the intensity levels of suprathermal particles (i.e., particles with kinetic energies >100 eV for electrons, >5 keV for protons) are higher, on average, than those near Earth.
For the electromagnetic radiation, that just decreases inversely squared with increasing distance from the source, as you would expect.