it's not explained in the game why the flowers are there, maybe it's just such a minor detail that they (the makers) didn't bother explaining it?

i agree i think its to do with as its a holy place and areith happens to be an ancient and she found the flowers grew in the place where maybe its a small gap in the lifestream where the holy water can rise to the surface this would then explain why at the end of AC the holy water rises out of the flowers and turns into a pool of healing water, this also shows how that 500 years later (end of VII begining of AC) midgar is reclaimed by the lifestream and flowers grow alll round the city. This could be also be shown as what arieth as an ancient is able to do once she has died, she is still there in spirit and over the years is able to return midgar back to its natural state how the lifestream and world once made it.

i like the holy water explanation. it makes the most sense (to me anyways)

Holy water/holy place sounds good for the Church. As for why they could grow outside Aeriths house, maybe the fact there is running water (if you look in the background, a mini waterfall) nearby could be the reason the soil is fertile enough for flowers.