If this apparent relationship between flares and decay rates proves true, it could lead to a method of predicting solar flares prior to their occurrence

So, can we predict the flares now? I've taken a look at Ephraim Fischbach's articles and it seems that we're very far from that, so the article you linked is interesting but overstates the facts by a lot. This is what I found the best explanation so far:

Some experiments seem to yield strong evidence of variability of beta-decay rates, but other experiments may show little or no such evidence. Some recent experiments help clarify the situation. In particular, a certain oscillation appears in neutrino measurements made at the Super-Kamiokande Neutrino Observatory and in radon beta-decay measurements made at the Geological Survey of Israel, with identical frequency (9.43 years ⁻¹ ), amplitude and phase, strengthening the case for an influence of neutrinos on beta decays. A review of current experimental information leads us to suggest that 1) beta-decay rates do not change, but 2) the angular distribution of decay products may be anisotropic, and 3) the angular distribution of decay products may be influenced by the ambient neutrino flux. It appears that experiments at standards laboratories tend to be insensitive to direction, and this may be the reason that they tend not to exhibit evidence of variability.

And even this I would take with a grain of salt