Firstly thanks for a question about Saki, one of my favourite authors sadly forgotten between Wilde and Wodehouse.
I think this is a matter of interpretation; I have read all of Saki's short stories multiple times, and I don't find Sredni Vashtar to be one of the darkest, or even dark at all. I think it's just a combination of two things:
Many of Saki's stories have a humorous opposition between a child (or young person) and an aunt or similar guardian. (Seen in Wilde and Wodehouse too.) The most satisfying example is in The Lumber Room, where Nicholas outwits his cousins' aunt (inimitably described by Saki as "the aunt-by-assertion" and "the soi-disant aunt"). But of course similar examples are scattered throughout the stories.
Many of Saki's stories use death humorously: in Esmé we have a boy being eaten by a hyena (feels morbid typing it here, but the story is hilarious); we have the same being discussed at great length by Clovis in The Quest; in Laura we have her joking about her death and then dying (sandwiched between two delicious sentences), The Unrest Cure is a joke about genocide written when it must have been absurd, and so on. (And minor examples abound, such as the death at the end of Tobermory.)
So, if you don't take the death of Conradin's guardian seriously, Sredni Vashtar is a typical Saki story: there's an imaginative boy (or sometimes it's a girl, as in the stories featuring Vera, most famously The Open Window); he's clever but the adults are rigid and oppressive; he has a world of his own (greatly amplified by his imagination) in which the adults have no admittance and would not understand anyway; and just once, he gets his satisfaction. What's not to like? :-)
I would not compare it to The Lord of the Flies, which I found truly dark and frankly will probably not read again. On the other hand, each time I dip into Saki it's pure joy and (somewhat horrified) laughter, and I don't think we need to consider stories like Sredni Vastar as being about the darkness in children. Saki's children are independent and consider themselves superior to the adults; any harm wished on the obtuse adults is purely secondary and comes from indifference or a wish to break free, rather than malice.
TL;DR: The fact that Sredni Vastar fits into a general pattern of Saki stories and characters means that we need not look for any special inspiration for it specifically.