How does the idea that ''Power is not fixed, it is fluid'' relate to Saki's "The Lumber Room"?

Power is, indeed, "fluid" in Saki's "The Lumber Room," as Nicholas skillfully manipulates the flow of power from his aunt to himself.
Nicholas initiates this flow when he tricks his aunt into adamantly insisting that no frog can be in his bowl of bread and milk. She reacts to the humiliating truth in an impulsive and retaliatory manner by forbidding Nicholas to accompany his younger brother and two cousins to Jagborough sands. While she believes she has gained the upper hand, Nicholas knows the children will have no fun at the beach because his cousin Bobby's boots are too tight. He gains a little power over his aunt when she asks, "Why didn't he tell me they were hurting?" and he informs her,

He told you twice, but you weren't listening. You often don't listen when we tell you important things.

The aunt asserts her power again, as she orders him "not to go into the gooseberry garden" because he is now "in disgrace."
This is her final victory, however, because Nicholas pretends he wants to enter this garden by feigning a look of "considerable obstinacy" that causes the aunt to feel she must assiduously guard the garden after the other children depart.
Although she has other matters to attend to, the aunt spends an hour or two puttering in this garden in order to keep a watch on the two doors of this "forbidden paradise." In the meantime, Nicholas, who has no interest whatsoever in the gooseberry garden, steals away to the lumber room. Having discovered where the key is, Nicholas opens the door and enters an oasis for his imagination. This room contains all sorts of intricate and interesting things, the "unimagined treasures" that stir the imagination and delight the aesthetic senses. One large item that catches the eyes and imagination of Nicholas is a large tapestry that depicts a hunter and the stag he shot with an arrow. The hunter's spotted dogs gather around this prey; however, in the background there are more than a few wolves entering the scene. A delighted Nicholas sits for "many golden minutes revolving the possibilities of the scene."
Soon, Nicholas is drawn to other objects that delight him: carved wooden boxes, ornate candlesticks, small brass figures, a book depicting beautiful birds—all sorts of beautiful things that he believes only someone like his aunt would lock away. After some time, he hears his aunt's voice shrilly calling out his name and ordering him to the gooseberry garden. The empowered Nicholas takes his time closing the book of birds, locking the door of the lumber room, and replacing the key.
As he leisurely strolls into the front garden, Nicholas's aunt calls his name again. He feigns ignorance of who he hears, asking, "Who's calling?" His aunt says she slipped into the rain-water tank. While the tank is empty, the slides are too slippery for her to get out. "Fetch the little ladder from under the cherry tree," she orders Nicholas.
In another triumph over his "self-asserted aunt," Nicholas informs her he has been ordered not to enter this garden. Then, as the exasperated aunt gives her permission now, the empowered Nicholas answers, 

Your voice doesn't sound like aunt's. . . you may be the Evil One tempting me to be disobedient. Aunt often tells me that the Evil One tempts me and that I always yield. This time I'm not going to yield.

Frustrated, the aunt tells Nicholas he is being ridiculous and insists he come to her aid. Nicholas decides to trick her when he asks if there will be strawberry jam at tea time.

"Certainly there will be," said the aunt, privately resolving that Nicholas should have none of it.

Again, Nicholas defeats her as he declares she must certainly be the "Evil One" because his aunt told him earlier that there was no strawberry jam. He walks away, leaving her in the water tank until a kitchen maid comes to the garden to pull up parsley and discovers the frustrated aunt.
More victory comes to Nicholas when the other children return from a miserable day at the beach because the tide was too high for them to play in the sand. Bobby's feet have also been in pain from his tight boots. When it is teatime,

[T]he aunt maintained the frozen muteness of one who has suffered undignified and unmerited detention in a rain-water tank for thirty-five minutes.

On the other hand, Nicholas revels in the enjoyment of strawberry jam, and his quiet victory of opening the lumber room where he experienced flights of fancy from the tapestry. Most of all, he delights in the power he exerted over his disgruntled aunt by turning all her authoritarian edicts into his own personal victories.