District energy systems represent a promising option for enhancing flexibility in electricity markets---an increasingly critical need given the rising frequency of both highly volatile and negative electricity prices. These price dynamics reflect a growing mismatch between electricity supply and demand. While price arbitrage between peak and off-peak periods---often associated with the so-called "battery wave"---has garnered attention, several barriers, including slow grid connection procedures, constrain the full integration of flexible resources into electricity markets. In this context, district energy systems are expected to play a vital role in providing flexibility and thereby formulating a future-proof business model since they are already implemented in field. This work proposes a systematic framework for assessing the flexibility potential of district energy systems in electricity markets. Central to this framework is a set of tailored Key Performance Indicators (KPIs) designed to capture the multifaceted contributions of district systems under uncertainty. The approach accounts for key sources of uncertainty, such as fluctuating electricity prices and weather-dependent operational constraints. Among others, the KPIs include: the utilization rate of available flexibility, the remaining flexibility reserve, electricity demand reduction compared to individual supply options, the difference in decision quality under uncertainty versus perfect foresight, and associated CO2 savings. The KPI framework is embedded within a two-stage stochastic optimization model, enabling optimal investment and operation decisions under uncertainty. Its practical applicability is demonstrated through a case study of a district energy system in Trondheim, Norway. The results provide novel insights into evaluating and strengthening the role of district energy systems as flexible assets in evolving electricity markets.