Generative enzyme design reduces wet lab costs by virtually screening high-reward variants of a wild-type enzyme from a vast, high-dimensional search space. This becomes particularly challenging when multiple substrates and reactions for the same enzyme yield complex reward functions, such as Enzyme Kinetic Parameters (EKP), compounded by increasing bio-safety constraints from stakeholders. This paper presents an integrated framework with a Generative Flow Networks (GFlowNets) model tailored for enzyme design and a fine-tuned protein language model for predicting EKP. Different from existing related work, our framework handles the complex EKP landscape introduced by the hydrolysis reaction mixture with the enzymatic reaction. By preliminary experiments, our framework shows it can generate high-reward enzyme variants under bio-safety constraints faster than alternative related methods.