Multiple-island endemics (MIE) are considered ideal natural subjects to study patterns of island colonization that involve recent population-level genetic processes. Kleinia neriifolia is a Canarian MIE widespread across the archipelago, which exhibits a close phylogenetic relationship with species in northwest Africa and at the other side of the Sahara Desert. Here, we used target sequencing with plastid skimming (Hyb-Seq), a dense population-level sampling of K. neriifolia, and representatives of its African-southern Arabian relatives to infer phylogenetic relationships and divergence times at the species and population levels. Using population genetic techniques and machine learning (convolutional neural networks [CNNs]), we reconstructed phylogeographic relationships and patterns of genetic admixture based on a multilocus SNP nuclear dataset. Phylogenomic analysis based on the nuclear dataset identifies the northwestern African Kleinia anteuphorbium as the sister species of K. neriifolia, with divergence starting in the early Pliocene. Divergence from its sister clade, comprising species from the Horn of Africa and southern Arabia, is dated to the arid Messinian period, lending support to the climatic vicariance origin of the Rand Flora. Phylogeographic model testing with CNNs supports an initial colonization of the central island of Tenerife followed by eastward and westward migration across the archipelago, which resulted in the observed east/west phylogeographic split. Subsequent population extinctions linked to aridification events, and recolonization from Tenerife, are proposed to explain the patterns of genetic admixture in the eastern Canary Islands. We demonstrate that CNNs based on SNPs can be used to discriminate among complex scenarios of island migration and colonization.