"get on like a house on fire" means you can really relate to another person and have things in common to talk about. Example: My neighbour and I get on like a house on fire because we love to talk about gardening.

When I had fire training at a previous job, we were shown a video of a house fire taking hold, to show how quickly a fire can take over (a worker had an accident with a heat gun). In under thirteen minutes the house was an inferno. Imagine getting along with someone that quickly! :)

My dad used to say it and it is little old fashioned. 'He met a new girl on the bus and they got on like a house on fire' means they liked each other and talked non-stop.