"..phenomena like solar flares can be predicted"
It depends on weather. Solar weather. And timescale.
BUT you cannot predict it's motion. Solar dot measure, any of this form - is unpredictable. It may go down, it may go up - both ways 50/50. Stochastical process. The process itself is non-linear. You can have solar weather in some bounded range, but you cannot say what it will be tomorrow. "Soft physics" works on such things. Still some unexplained things, same as in meteorology.
"could be used to predict its supernova explosion"
Yes. Direct observation of star could be useful. From close range. With magnetometric, X-ray etc. Which none of us have. On the other hand, supernova relies on changes in chemical constituents in star material. It could be defined.
"but I'm looking for times that are orders of magnitude longer than those discussed there". Yes, there is. Chain of events starts with changes in spectrum, which corresponds to changes of chemical structure in star material. Knowing all star parameters (from close range), you can have the time until event. Ofc you cannot definitely say what follows, because small changes in parameters are varying outcome --- either there will be white dwarf or neutron star etc.
Ofc you cannot compute exact second of event, because (first) there is no such thing. Event occurs continiously. And, second, your prediction will rely on existing star models, and equipment accuracy. So if you measure with accuracy of 2%, do not expect prediction be more precise then 2%. Common practice shows that model makes more miscalculations almost always (99% of events miscalculated are from wrong models and/or miscalculated model range).
Consider weather prediction. It fails. When it fails, nobody notices. Because it fails when model fails. It fails less often then it works, but it happens. It doesn't fail catastrophically, that's why nobody notices. "Oh, it's more colder at 4 o'clock, but prediction said it will get colder at 2 o'clock" - nobody says that. It happened anyway, but model was slightly out of range.
PS. Also categorize exactly what prediction means. Because there is still no such thing as "prediction". In science, we say that "time period until Moon falls on Earth is 200-300 billion years". Always in range. According to model. And according to data.