Generative models see increasing use in computer-aided drug design. While performing well at capturing distributions of molecular motifs, they often produce synthetically inaccessible molecules. To address this, we introduce SynFlowNet, a GFlowNet model whose action space uses chemical reactions and buyable reactants to sequentially build new molecules. Using forward synthesis as an explicit constraint in our algorithm bridges the gap between in silico molecular generation and real world synthesis capabilities. We evaluate our approach using synthetic accessibility scores and an independent retrosynthesis tool to assess the synthesizability of our compounds, and motivate the choice of GFlowNets through considerable improvement in sample diversity compared to baselines. Furthermore, we leverage GFlowNets' parameterizable backward policy to address shortcomings of SMARTS encoding in the MDP design, enabling the model to retrieve synthesis pathways for unseen molecules.