Where an external pipe or gully has genuinely frozen, gentle warming rather than boiling water is the right approach — boiling water on frozen ceramic or old pipework can crack it.
The underground system rarely freezes because it sits below frost depth, so a winter blockage is almost always a normal blockage rather than an ice one.
Christmas and New Year are peak season for kitchen drain failures. If your kitchen sink is already slow in December, deal with it before the cooking starts.