Gout is an inflammatory metabolic disease characterized by hyperuricemia and the deposition of monosodium urate crystals. In this study, an integrated network pharmacology and molecular docking approach was used to assess the phytoconstituent compounds of Ficus religiosa and Psoralea corylifolia as potential anti-gout agents. Predicted targets obtained from SwissTargetPrediction and disease databases were intersected to generate a focused set of proteins, which were analyzed using STRING, Cytoscape topology, and molecular complex detection clustering. Gene ontology and Kyoto encyclopedia of genes and genomes enrichment analyses highlighted pathways regulating urate transport, inflammatory signaling, and oxidative stress. A total of 19 phytoconstituents were screened in silico, with seven (corylin, lupenone, methyl oleonolate, lupeol, bavachinin, stigmasterol, and β-sitosterol-D-glucoside) exhibiting favorable binding affinities (≤−8.0 kcal/mol) against the human urate transporter (GLUT9), interacting with residues involved in urate handling. Absorption, distribution, metabolism, excretion, and toxicity profiling showed relatively low oral absorption prediction, variable clearance, and compound-specific toxicity concerns, while the prediction of activity spectra for substances analysis suggested potential anti-inflammatory activity. These findings indicate that urate metabolism and inflammation can be modulated by the plants’ phytoconstituents and highlight the need for targeted in vitro, in vivo, and formulation studies to ascertain efficacy and address bioavailability and safety concerns.