Are normal cooking thermometers suitable to use as tea thermometers?

The flexible generalist thermometer of the kitchen, the instant read thermometer, should be quite suitable measuring the temperature of the water for tea brewing. It covers the right range, has reasonable accuracy, and responds relatively quickly.

You can get traditional ones such as the classic Taylor model very inexpensively, or high quality electronic ones such as the Thermapen, as well as a large number of mid-range models that offer excellent value, accuracy, and reasonable response time.

Many come with a clip that would allow you to set them on the side of a pot, but you would not attach them to kettle. Instead, you hold them in, and they register the temperature in a few seconds (depending on the model)—thus the name, instant read.