New opportunities and challenges arise in power system operations due to the energy transition from fossil fuels to renewable energy resources coupled with the liberalization of electricity markets. These opportunities appear in the form of energy flexibility, and the uncertainty of renewable generation challenges power system security of supply. This paper presents an efficient energy management model that considers available flexibility from active industrial networks connected to the power distribution grid. Installation of storage units in the industrial grid provides flexibility. The goal is to solve a multi-objective optimal power flow problem to reduce system costs and carbon emissions. In the proposed two-fold approach, Tchebycheff's decomposition method breaks down the multi-objective problem into scalar subproblems, which are then singularly minimized using a distributed gradient projection algorithm. Distributed computation helps retain the data privacy of each participant. The algorithm is applied to modified IEEE radial test network to demonstrate achieved cost benefits and carbon footprint reduction.