The development of alternative anticancer agents with minimal side effects has become more critical due to the rising recurrence of mammalian malignancies and the severe side effects of chemotherapeutic treatments. Kinases are an essential target for neostatic impact as they play an important role in the modulation of growth factor signalling. Our work aims to screen novel nine-series of thiazole-based aminopyrimidines and sulphaminopyrimidines against the enzymes mitochondrial thymidine kinase 2, deoxyguanosine kinase (2OCP), deoxycytidine kinase (2QRN) and thymidylate kinase (1E2Q) by molecular docking, synthesise and to study their in vitro inhibitory studies. The synthesised compounds were characterised by Infrared, Nuclear magnetic resonance and Mass spectroscopy. In silico studies, compound 4c stands out among the series, with a reported docking score ranging from −6 to −8 Kcal/mol against all the analogue kinases. The in vitro cytotoxicity assay against human small-cell lung carcinoma (A-549) has shown that 5c (IC50 = 53.9 µM) has an excellent cytotoxic effect over 4c (IC50= 68.68 µM). The reason might be the presence of the benzene sulphonamide group, which enhances their anticancer action. To conclude, the compounds 4c and 5c were found to be potent inhibitors of the deoxynucleoside kinases. In vivo studies must further verify these to prove their potent neostatic effect.