It is quite possible, though you haven't clarified the atmospheric conditions, that what you've been observing are electrical discharges called "sprites", e.g.
According to a Wikipedia entry: "Sprites are large-scale electrical discharges that occur high above thunderstorm clouds, or cumulonimbus, giving rise to a quite varied range of visual shapes flickering in the night sky. They are triggered by the discharges of positive lightning between an underlying thundercloud and the ground."
In contrast, what we call flares are detected as explosive eruptions on the Sun (solar flares) in which a vast amount of magnetic potential energy ("free energy") is stored until released by a process called magnetic reconnection. Technically speaking one need not have magnetic reconnection to qualify for a flare. However, one would need to have at least a magnetic mirror system in place, and this should include structures called double layers, which basically act like capacitors to store electrical energy across large potential drops.
If the voltage drop is large enough, one can observe flare conditions. According to Alfven ('Cosmic Plasma', 1981), any double layers within regional "separators" will explode before a saturation level of current is reached such that:
I_s = [V(b) – V(D)] / R
where V(b) = L(dI/dt) + RI
with L the inductance, and I the current, R the resistance and the flare power can be estimated using:
(P) = I V(D)
where V(D) is the voltage across the double layer. The problem with the Earth flare hypothesis is that it is impossible to see how a magnetic mirror system would operate for it, given the low altitudes at which the phenomenon appeared to be seen by the observer(s) you cite. No magnetic mirrors, no likely Earth flares!
Also, you stated having formed a hypothesis but merely making observations and then a conjecture based on them does not constitute such. What are the key elements of it? How will you test it? What indicators for the test will show the phenomenon is an Earth flare? What observations will you require to support that? What observations will falsify it? What are the necessary and sufficient conditions for an "Earth flare" to occur or exist?
Right now, all you really have is a constellation of peculiar observations or anomalies to which you have attached some significance or physical meaning via intuition (for lack of a better word) but devoid of any formal measurements you yourself have performed. When you perform those measurements, or at least publish the photographs of the assorted phenomena (YOU have taken), I will be more inclined to take "Earth flares" as something substantive and distinct and not merely another UFO manifestation.
Again, 'UFO' is not intended as a putdown, but a simple statement of fact of what you actually have here, minus any compelling data of your own or photos, measurements. These latter might enable a more quantitative basis for analysis and even working out a model for your "Earth flare".
Even if you can't provide a model, you should still be able to at least hypothesize based on observations-data that you yourself obtain. It is all very well to go back to historic sightings, magnetic records, but these still don't make the case that an entity such as an "Earth flare" really exists.
Note also when one uses the term "flare" one means something specific in a context of rapid emission of energy. This applies to every case for a genuine solar flare or what we understand by such. I see no comparable basis to make a similar claim for Earth flares.
I encourage you to keep on with your observations of assorted optical phenomena. In one of my original papers I referred to "transient optical phenomena of the atmosphere" - which paper you might find useful to read, e.g.