Trincó is the past tense of the verb trincar, which is a colloquial and somewhat informal way to say "to bust," "to nab," or "to catch someone in the act," often in a negative or illicit context.
In the song, it's used when an agent catches someone who stole the president's car: "Llega un agente y lo trincó" (An agent arrives and busted him). It's a vivid and less common word than arrestar (to arrest), making it more engaging and memorable.
"Una Historia de Tantas" builds its verses on the Spanish word "tanto," meaning "so much" or "so many." Melendi lists a string of small, everyday contradictions: throwing a stone and hiding the hand that threw it, singing to the moon until you fall for it yourself, chasing love in hotels and parties that never really deliver it. Each line is its own tiny proverb about excess and hypocrisy.
The chorus turns those "so many" small things into one saying: the jug goes to the well so many times that it finally breaks. It's the Spanish version of "one too many trips to the well," a warning that a habit repeated too often eventually catches up with you.
The story that follows makes the idea literal. Someone tries to do a good turn, or maybe just a bit of mischief, with a car parked on a bridge, and gets arrested for it, not realizing the car belonged to the president. It's a wry little parable about the ironies life keeps handing us: so much noise for so little sense, so many good intentions gone wrong.