Puckoon is a blurt of Spike Milligan's rapid-fire childish cleverness and is very much of its time, it was written in 1963.
It is (as far as I can gather, discerning the plot through the maze of little gags takes quite an effort) the story of a small town which lies right at the place where the officials have decided to run the new Irish borderline. This creates situations like, a small corner in the local pub in one country being in one country and having lower taxes on alcohol than the rest of the pub, so a squish of cheapskates clamour for drinks from that spot while the rest of the pub is empty.
With much silliness on every page, no characters get the time to really build up a personality, with a cast of over 50 people in the slim paperback. Every single event is the precursor to a one-liner or a surreal throwaway. Some of the jokes raised a smile, but at the heart of it seems to be a disdain for the general populous, a sexist approach and you feel that Spike in his sandbox is just doodling with words. E.g "The door opened, a girl's face appeared, it appeared very pretty too."
Look, it's clever, but it's not the medium for Spike in my opinion.
He clearly had a wonderful, probably autistic, precious mind for humour, and it must have been hard for him during his manic times, not to crack jokes about every single thing he saw or heard, making for a noisy mind and probably maddening himself and those close to him.
But put him together with other sympathetic and guiding lights such as the Goon Show cast, and this hyper-jocularity suddenly has a place among other characters and talents, and becomes more effective.