Trouble with first part of Experiment 11 (Make: Electronics) when using multimeter
Obviously your multimeter influences your circuit. To measure the voltage across the capacitor some current must flow through the multimeter. The amount of current through the multimeter is defined by the measured voltage and the internal resistance of the multimeter.

With the high resistor value of \$470 K\Omega\$ even an internal resistance as high as \$1 M\Omega\$ has a remarkable impact on your circuit.

When you have the parts at hand, you could change your circuit to use \$47 K\Omega\$ and \$22 \mu F\$. The time from flash to flash shouldn't change. However the flash duration would be 10 times longer.