This appears to have been a favorite technique of Diaghilev's. Earlier, he did the same with Massine, who had been hesitant to attempt choreography until he looked closely at a painting of The Annunciation by Simone Martini, in the Uffizi .. and felt the calling.
Taper described in his Balanchine bio how during one summer break, Diaghilev led a mini-tour of Italy with a handful of the company and taught Balanchine about visual art.
Although Balanchine invented the character of The Siren in Prodigal son, he may have also been thinking of depictions of the Temptation of Eve, several of which show The Serpent winding its coils around Eve (and even around Adam). The Siren, usually danced by a long-legged dancer, mimics both seduction and enslavement. Below is a link to William Blake's version. Substitute a male figure for the Eve figure, and you have a version of Prodigal Son.
On the other hand, according to Agnes de Mille (as quoted by Taper), the pas de deux between Siren and Son may have been based upon a circus trick.
For this ballet Balanchine turned away from the classical vocabulary he had employed in Apollo, but her remembered the lesson he had learned about unity of tone. This time his palette of movement contained borrowings from gymnasts, circus performers, and acrobats. In an interesting article, "Acrobatics and the New Choreography," ... Agnes de Mille discussed some of these devises and the uses to which Balanchine had put them: the circus trick employed in the duet betwen the Siren (Doubrovska) and the Prodigal Son (Lifar) -- "one of the most important seductions to be found on any modern stage," she wrote -- in which Doubrovska wraps herself around Lifar's waist like a a belt and then slides slowly down his body to the floor where, as he sinks down beside her, their limbs intertwine in an inextricable tangle ...