The charge controller chip on the MKR GSM 1400 is the BQ24195L. The "CHRG" LED is connected to its "STAT" pin. The behavior of the STAT pin is described in table 8.3.4.1 of the datasheet:

CHARGING STATE | STAT

Charging in progress (including recharge) | LOW
Charging complete | HIGH
Sleep mode, charge disable | HIGH
Charge suspend (Input over-voltage, TS fault, | Blinking at 1Hz
timer fault, input or system over-voltage)

So there are a number of things that can cause blinking. There is a charge timer that automatically stop the charge after a specific amount of time if the battery is still not detected to be fully charged. The idea is to avoid creating a dangerous situation by overcharging the battery if something has gone wrong. If you have a battery connected that has a capacity that causes it to not be fully charged after the safety timer duration, the timer would time out and the LED would blink. You should be able to identify if the blink is caused by the safety timer by timing how long it takes before the blink occurs.