Yes, to measure how much power the board is consuming you would put an ammeter in series with the power supply, or use a power supply that has one built in.
If you wanted to measure how much power the Epiphany chip is consuming, you would have to intercept its power supply and I'm not sure if that is easily doable, but you could always take a look at the
AFAIK there isn't any capability within the Epiphany that would let you measure energy consumption at a core level.
If you are looking for a low cost and high accuracy / high sample rate energy measurement solution, I can recommend the (disclosure: I'm involved with the project).
Regards,
Andrew