Can I use someone's Apple ID Email to Text Them on Their iPad if I Don't Have an iPhone?
Yes, you can send a text message to your friend using your Amazon Fire, to their iPad, but only if they have an iPhone as well. 

If they do, then your message will either go SMS (Short Message Service), which is basically what you know as a text message, or MMS (Multimedia Message Service), which is what gets sent when you send a photo to a friend with a text messaging app.

Your friend will need to have iMessage set up on their iPad, and they will need to have an iPhone as well in order to receive SMS/MMS messages from someone not on iMessage. 

The setting for this is actually in the iPhone's settings. It will not matter if you send it through an email address or a telephone number, if they do not have an iPhone, and you are not sending the text through iMessage, their iPad will not get the message. If you had an iPhone or iPad or Mac with iMessage on it, then you could in fact send text messages to one another via iMessage, as those messages travel exclusively on Apple's network.

I do not know for sure, but I have a feeling that SMS/MMS go through the Mobile Network Provider's system and only gets to Apple's iMessage network when it goes from the Mobile Service to the iPhone, which then can reroute it to iMessage and then to the devices linked to that iPhone.