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The flag is actually supposed to show the island's links with Cuba, rather than the US. Consider the Cuban flag:
The flag of the Commonwealth of Puerto Rico is basically the Cuban Flag with the red and blue colours reversed.
According to one tourist site, the symbolism is as follows:
The white star stands for the Commonwealth of Puerto Rico while the three sides of the equilateral triangle together represent the three branches of the Republican government (executive, legislative and judicial branches). The three red strips symbolize the blood that feeds those parts of the government. The two white stripes symbolizing the rights of man and the freedom of the individual, are a perpetual reminder of the need for vigilance of a democratic government is to be preserved.
Of course, that may be a later "re-interpretation" after Puerto Rico became a Commonwealth in 1952.
Just for completeness, according to Wikipedia, the symbolism of the Cuban flag is
The three blue stripes represent the three departments in which Cuba was divided at that time, the white purity of ideals, the light; the red triangle, originating from the French Revolution β and the three ideals of liberty, equality and fraternity: red for the blood and the courage; the star was the new state that should be added to the United States.