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The radial-dependent positions of snowlines of abundant oxygen- and carbon-bearing molecules in protoplanetary discs will result in systematic radial variations in the C/O ratios in the gas and ice. This variation is proposed as a tracer of the formation location of gas-giant planets. However, disc chemistry can affect the C/O ratios in the gas and ice, thus potentially erasing the chemical fingerprint of snowlines in gas-giant atmospheres. We calculate the molecular composition of hot Jupiter atmospheres using elemental abundances extracted from a chemical kinetics model of a disc midplane where we have varied the initial abundances and ionization rates. The models predict a wider diversity of possible atmospheres than those predicted using elemental ratios from snowlines only. As found in previous work, as the C/O ratio exceeds the solar value, the mixing ratio of CH$_{4}$ increases in the lower atmosphere, and those of C$_{2}$H$_{2}$ and HCN increase mainly in the upper atmosphere. The mixing ratio of H$_{2}$O correspondingly decreases. We find that hot Jupiters with C/O$>1$ can only form between the CO$_{2}$ and CH$_{4}$ snowlines. Moreover, they can only form in a disc which has fully inherited interstellar abundances, and where negligible chemistry has occurred. Hence, carbon-rich planets are likely rare, unless efficient transport of hydrocarbon-rich ices via pebble drift to within the CH$_{4}$ snowline is a common phenomenon. We predict combinations of C/O ratios and elemental abundances that can constrain gas-giant planet formation locations relative to snowline positions, and that can provide insight into the disc chemical history.