As @Musharib said, it shouldn't. I assume that the app uses push notifications or sms under the covers, so it *should* only use what it absolutely needs, and because streaming video isn't in the picture you should be good. read more
It depends on if you use kick a lot. If you use it a lot, there is a possibility that it will use a lot of data, especially if you store these messages locally. However, I have found that messaging apps do not usually take up a lot of space. read more