Hi Netraven,
i guess the best way in assessing the significance of the gill flicking is to determine how frequently the gill flicks are (the interval time), the duration of such sessions (isolated incident or chronic continuous) as well as if there are other accompanying signs of illness or stress.
Occasional random gill flicking whereby the axie looks relaxed and shows no sign of ill health or stress is normal. This is the facilitate gaseous exchange around the gills.
Very frequent gill flicking of prolonged duration is not normal. This could be a sign of oxygen deficit in the environment (check tank parameters, temperature, aeration), indication of a terminally ill axie, or ongoing chronic pathology such as anaemia or even a form of axie 'tuberculosis'. Normally, this would accompany other tell tale signs like inappetance, unusual behaviour, curled tail tip etc.
Cheers.