Yes you can. There are a number of texting apps that you can get from Amazon store. There is one major consideration. If you want to text from you tablet with your cell phone number, then the tablet needs to be connected to the phone (wifi or bluetooth) while doing that. Otherwise you will need to text using a email address or another phone number. I choose the later and use Textme. Works well for me.
Also understand that anytime you use an app, you are giving up some privacy. In this case the contact and texting contents will be collected by the app.
Mostly read with my Kindle Fire. Although you can text and email on them I don't thing that they are designed to do those things. Clumsy but doable in my mind