In the dry regions of Chile, prolific flowering from forest plantation is particularly advantageous for honey production, in order to supplement the erratic flowering in native plants. Eucalyptus cladocalyx is a species suitable for areas with low water availability and their flowers provide a reliable source for the production of honey. The aim of this study was to examine the heritability of flowering intensity in 49 open-pollinated families of E. cladocalyx in southern Atacama Desert, Chile, with the view to the selection for prolific flowering, but with minimal impact on precocious flowering. The Bayesian variance component estimation model was assumed using the Gibbs sampling algorithm. Threshold models were fitted to flowering data (bi-character model). Flowering intensity was found to be highly heritable (posterior mean: h (2) = 0.48; and credible interval: 0.41-0.56). The posterior mean of the genetic correlation between flowering precocity and intensity was positive (r = 0.45) and according to the credible interval (0.341-0.542), it was significantly different from zero, indicating that selection on breeding values of early flowering at age three, would have significant and positive impact on flowering intensity 5 years later (or in 8-year-old trees). These results are important for the start of a small-scale breeding program for the species in southern Atacama Desert. The genetic variability found in these breeding populations may be used for breeding purposes in regions where arid environmental conditions are limiting to the establishment of eucalypts trees.