# Then they

"Then people" or "Then the Egyptians". These are Yahweh's words about Egypt.

# they will know that I am Yahweh

"they will understand that I am Yahweh, the one true God". Yahweh implies that they will know he is the one true God who has supreme authority and power. See Ezekiel 6:7. 

# when I set fire in Egypt

"when I send an army to burn Egypt with fire"

# all of her helpers are destroyed

"I destroy all of the allies of Egypt" or "when armies destroy all of those who help Egypt"