Participation in residential energy demand response programs requires an active role by consumers. They contribute flexibility in how they use their appliances as the means to adjust energy consumption, and reduce demand peaks, possibly at the expense of their own comfort (e.g., thermal). Understanding the collective potential of appliance-level flexibility for reducing demand peaks is challenging and complex. For instance, physical characteristics of appliances, usage preferences, and comfort requirements all influence consumer flexibility, adoption, and effectiveness of demand response programs. To capture and study such socio-technical factors and trade-offs, this paper contributes a novel appliance-level flexible scheduling framework based on consumers' self-determined flexibility and comfort requirements. By utilizing this framework, this paper studies (i) consumers' usage preferences across various appliances, as well as their voluntary contribution of flexibility and willingness to sacrifice comfort for improving grid stability, (ii) impact of individual appliances on the collective goal of reducing demand peaks, and (iii) the effect of variable levels of flexibility, cooperation, and participation on the outcome of coordinated appliance scheduling. Experimental evaluation using a novel dataset collected via a smartphone app shows that higher consumer flexibility can significantly reduce demand peaks, with the oven having the highest system-wide potential for this. Overall, the cooperative approach allows for higher peak-shaving compared to non-cooperative schemes that focus entirely on the efficiency of individual appliances. The findings of this study can be used to design more cost-effective and granular (appliance-level) demand response programs in participatory and decentralized Smart Grids.