Siri and many other apps have a speech to text application which I'd like to be able to have transferred to a small LED display. In other words speak to the device and have the printed words of your speaking displayed on the LED. Can anyone point me in the right direction or have advice?

Why an LED screen, why not an LCD like on a phone?
Will this device have Internet connectivity or will processing need to be local?

local; no need for internet- but if I could transmit the text to the LED screen wirelessly that would be better. LED is better for night viewing, so I think LED is better but if LCD is tough and well viewed in dim light that would work as well.

The second part is the speech to text. If I could have say, 10 phrases which are already "printed out" (on the smart device) be able to put on the remote LED display with my device then the second part is to be able to make infinite choices by the speech to text.

Is this for a car's back window?

store front and yes ... for a car window.

I was thinking the same thing. There are many times when that would have been fun to have.

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All you should need is a Lightning to HDMI adapter cable. Apple make one, check their online store.

Lightning Digital AV Adapter - Lightning to HDMI - Apple