How to boil milk for a cup of coffee without a pot?
Kettle sounds reasonable, but it's difficult to clean it after use.
Microwave is your best bet. If it exploded last time, it might have been the container. First, get a new container and test that it's microwave safe. Add your milk and a few coffee grounds to create a non-uniform volume so it won't get superheated. Nuke until boiling.
If you don't want to go the microwave route, I can think of an alternative but it takes a while and won't technically boil the milk but it will get it pretty close. Put your milk in a container and place that inside a larger container (like a cup inside a big measuring bowl). Boil water through your favorite means and pour it into the large container. Stir a bit and wait for the heat transfer. Repeat with fresh boiling water until the milk is hot enough. I use this to heat frozen breast milk - not to boiling, of course - and it works but it's tedious. Microwave is still the way to go for a daily routine.
My favourite method, in absence of microwave, is to place your mug directly onto electric oven stove.
For example to make a coffee, add instant coffee and pour into your mug boiled water (e.g. kettle) to warm your mug (1/3, 2/3 or optional), pour the milk (other rest), place the mug on the stove and set the heat to minimum power (otherwise your mug could break of heat) and relax. It's a bit slower method, but having your whole mug hot, your coffee stay warm for longer. See example:
Or if you don't have electric oven, buy a alcohol stove (such as Zelph Starlyte Stove).
Or create your own. Here are the instructions:
Super Cat Alcohol Stove
Find or buy some small cheap food in aluminium can, e.g. cat food.
Empty the container (by giving to your neighbour's cat if you don't have) and make some small holes as below.
Add some fuel or alcohol (e.g. spiritus) and set on fire (on some safe ground).
Source: Super Cat Alcohol Stove at Frontage Roads
Try powdered milk. Boil the water in the microwave in a cup, then add the powdered milk afterward. Usually, powdered milk has a poor taste only when drinking it straight. When used as an ingredient or mixing there is usually no poor taste.