My firestick won't work on my tv. It's a Vizio HDMI model #D40-41.

There cold be something wrong with the HDMI ports or the HDMI cable then or there might be a problem with your firestick then. Try a new firestick and a new HDMI cable to see if that helps.If the TV's screen is still flashing then there is a problem with the back light and the LCD for your TV.

This should be an easy fix, on your firestick remote select the home button, then settings then display and set it to automatic this way the firestick will adjust to your TV res.

Sounds like the TV doesnt recognize the Firestick as an HDMI source. Or the Firestick isn't getting power. Or the Firestick is broken.
Does the firestick work in the HDMI port the DirectTV is currently in?

If it works on your other TVs then the Firestick is OK, which means the problem is with that particular TV. Does the TV have more than one HDMI port? Have you tried the others?

At a guess, the TV may not be providing sufficient peripheral power on the HDMI port. https://www.quora.com/How-many-volts-does-an-HDMI-port-put-out

When you used directv how did you get the signal? was it automatic? if so the firestick should work. Are you sure you getting power to the firestick. I have had problems in the past using the USB for Power that is on the TV. I always plug the usb power from the Firestick to an outlet instead of the USB power if available on the TV.

I switch from firestick to live TV by using the television's remote control. Its located under the "input" button. Select between tv, HDMI 1 though 4, (my firestick is on HDMI-3), video-1, and DVD.

This will mean that your TV will only accept 1 HDMI signal through that port meaning a splitter won't work unfortunately.
The only other option is to get an adaptor for another port that you do have spare on your TV, like AV or DVI.

Plug the fire TV stick into a HDMI port on the TV. Plug in power for firestick. Change the INPUT to that HDMI port Main firestick screen should appear after 10-20 seconds

1. Plug your Firestick into one of the HDMI ports on your TV. Plug the USB power cable into your Firestick and into the wall or a USB outlet on your TV (if there is one)
2. Turn on your TV and set the INPUT device to the correct HDMI port. There should be a splash screen or setup screen on your TV at that point.
3. Using your Firestick remote, navigate to network settings and scan for your WI-FI router, Then enter the Wi-Fi password for your router (the same one you use for your smart phone or laptop).

You should be able to fully use your Amazon Firestick, and if you have Amazon Prime, be able to access all prime and free offerings from Amazon.

It means there is no signal appearing at the HDMI 4 port of the TV, This could be because the Firestick is unplugged, or not working.
Repairlass1989 posted a suggestion to Additional Information that sounds good so I will repeat it in the Answer:
Repairlass1989 Nov 08, 2019 Unplug your tv and fire stick all together for 10 minutes after 10 minutes plug the tv and fire stick back in goto source hdmi channel and it should work had the same problem