Power systems with increasing flexibility requirements are increasingly relying on gas turbines to follow the net-load and the gas network to support unforecast changes in gas turbine generation. In addition, the role of the gas network in supplying fuel for the heating sector means that alternative heating scenarios can impact the gas network's ability to provide this flexibility. In this light, this paper presents a novel methodology for the assessment of the impact of heating on the integrated flexibility of the gas and electrical transmission networks. The model considers the transport requirements of gas for the heating sector as well as the regional distribution of gas within the gas network in the context of zonal linepack distribution. Electrical network modelling is conducted using a DC OPF while the gas network flexibility is assessed using a novel iterative steady-state gas flow methodology. Case studies are performed on the British networks and highlight how in energy systems with a large heat-based gas demand then extreme cold days can reduce the flexibility of the gas network while, on milder days, the use of gas turbines in supplying an electrified heating sector can lead an increase in linepack swing.