You cannot get specific values, but you can estimate roughly how many they have acquired.
Go into the Pokemon's Summary page, and press Y. The central bright yellow area is the base stats of the Pokemon, while the outer dark gold color represents the EVs the Pokemon has acquired. When the Pokemon has maxed out it's EV total at 510 points, the dark gold color will turn blue. When a specific stat has reached it's max of 252, it will acquire some sparkles around it.
Additionally, JasonE is correct, there is a woman in the Battle Royale lobby who will check whether the Pokemon in question has reached it's 510 total EVs yet or not, and if it has, will give the Pokemon the Effort Ribbon.