What type of plot development or plot diagram ("chain", " a fork", "ring"...) is used in the story "The Golden Kite, The Silver Wind" by Ray Bradbury?

I must admit as to being unsure precisely what you are
referring to in terms of the different plot diagrams that you mention. However, I wonder
if the "chain" that you refer to could indicate a chain linking different events to each
other. What is clearly evident from this story is the way that cause and effect operates
to create the continual rebuilding of the city walls as each city vies with each other
for dominance. Note how the beginning of the story feels compelled to rebuild his city
walls so that the "pig" that the other city's walls resemble will not "devour" the
orange that the Mandarin's city's walls resemble:

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Demons lurked everywhere, Death swam in the
wetness of an eye, the turn of a gull's wing meant rain, a fan held so, the tilt of a
roof, and, yes, even a city wall was of immense importance. Travellers and tourists,
caravans, musicians, artists, coming upon these two towns, equally judging the portents,
would say, "The city shaped like an orange? No! I will enter the city shaped like a pig
and prosper, eating all, growing fat with good luck and
prosperity!"

Thus the chain
analogy seems to be most fitting. Each change of the city walls provokes a change in the
city walls of the other city, until only the common sense of the Mandarin's daughter
saves both of the cities from destruction.