The number of distributed energy resources installed in distribution networks is steadily increasing. Their flexibility can be leveraged by aggregators and used in the wholesale markets. However, the utilization of this flexibility cannot neglect the operating conditions of distribution networks, and thus some form of coordination between distribution and transmission system operators must exist. The idea of operating local flexibility markets has been proposed to address these issues, but experience from real-life demonstrations is still missing. The Danish project EcoGrid 2.0 has designed, implemented and tested a local flexibility market with 800 participating customers, which runs in parallel with the wholesale markets. First, this paper presents a method to identify and quantify the value of possible flexibility services that are beneficial to the distribution system operator. Next, it provides insight from the operation of a real local flexibility market, with a large number of controllable loads. Results show that aggregators are able to reliably shape the load of residential heating units to deliver flexibility services, despite the presence of large uncertainties. Services can act as an insurance policy against rare but consequential network overloadings and outages. In these rare cases flexibility services can increase social welfare significantly. However, such services should be carefully selected to avoid adverse effects. Finally, we provide with guidelines and some general remarks on the nature and the desirable characteristics of those markets and services.