Recent floods in America, Europe, Asia and Africa reminded societies across the world of the need to revisit their climate adaptation strategies. Rapid urbanization coinciding with a growing frequency and intensity of floods requires transformative actions in cities worldwide. While abandoning flood prone areas is sometimes discussed as a public climate adaptation option, little attention is paid to studying cumulative impacts of outmigration as an individual choice. To explore the aggregated consequences of households' outmigration decisions in response to increasing flood hazards, we employ a computational agent-based model grounded in empirical heuristics of buyers' and sellers' behaviour in a flood-prone housing market. Our results suggest that pure market-driven processes can cause shifts in demographics in climate-sensitive hotspots placing low-income households further at risk. They get trapped in hazard zones, even when individual risk perceptions and behavioural location preferences are independent of income, suggesting increasing climate gentrification as an outcome of market sorting.