I believe that there are no downside to solar flares, that the energy bonus starts when you are click on the notification and runs for a set amount of time from the initial notification (so clicking quickly on it is good), and that the amount of energy bonus per time is fixed and there is no way of changing it.
So the ideal strategy is to just treat solar flares as an unexpected energy bonus and collect it as soon as you are notified.
I don't normally find that lack of energy in Startopia is a problem, but that is because I use other tactics to increase income. At the start of every level, I pause the game and then set the prices charged by the spaceport, slumberpods, din-o-mat, lavatron, and any other structures used by tourists to their maximum (doubling income from them). The only effect I notice from doing this is to make tourists leave the station faster when they run out of money. This also means I have to be faster when hiring tourists I want to keep (before they leave the station), and the higher tourist turnover eventually also requires a 2nd spaceport to handle the added traffic flow. I find that higher prices don't seem to keep the tourists from making purchases though.