To get on like a house on fire is to take to each other immediately and warmly. They got on like a house on fire, we get on like a house on fire.
The image is speed rather than destruction, since a thatched house burnt very fast indeed. It describes a friendship that started at once, which is what makes it a compliment to both people.
1phraseget on like a house on fireTo take to each other immediately and warmly.
“I was nervous about meeting her parents, but now we get on like a house on fire.”
get on like a house on fire is a friendship.
From the speed with which a house, particularly a thatched one, would burn.
By metaphor, reflecting the notion that housefires are archetypally roaringly quick and robust.
Etymology from Wiktionary, CC BY-SA
Practised in Idioms