Angiosperms possess various strategies to ensure reproductive success, such as stylar polymorphisms that encourage outcrossing. Here, we investigate the genetic basis of one such dimorphism that combines both temporal and spatial separation of sexual function, termed flexistyly. It is a floral strategy characterised by the presence of two morphs that differ in the timing of stylar movement. We performed a de novo assembly of the genome of Alpinia nigra using high-depth genomic sequencing. We then used Pool-seq to identify candidate regions for flexistyly based on allele frequency or coverage differences between pools of anaflexistylous and cataflexistylous morphs. The final genome assembly size was 2 Gb, and showed no evidence of recent polyploidy. The Pool-seq did not reveal large regions with high FST values, suggesting large structural chromosomal polymorphisms are unlikely to underlie differences between morphs. Similarly, no region had a 1:2 mapping depth ratio which would be indicative of hemizygosity. We propose that flexistyly is governed by a small genomic region that might be difficult to detect with Pool-seq, or a complex genomic region that proved difficult to assemble. Our genome will be a valuable resource for future studies of gingers, and provides the first steps towards characterising this complex floral phenotype.