We don't support Steam Play on Linux officially yet, but we've received some positive feedback on ProtonDB.
You can install and play House Flipper on your Linux PC if you enforce the option through House Flipper's Steam properties.
The option you're looking for is called "Force the use of a specific Steam Play compatibility tool" (at the bottom of the properties window).
If the option is missing
You may need to enable Steam Beta Update.
In Steam Settings's Account tab click the "Change" button in "Beta participation" section and enable "Steam Beta Update" in the next window.
