Transmission light blinks when I accelerate to a certain speed

Hello,

The transmission light blinks when there is an error code within the transmission module.

So, when it happens does the vehicle drive different?

Best course of action would be to scan the vehicle with a scanner that is capable of retrieving transmission trouble codes. This can help identify what might be the issue.

Here is a guide that will help with this:

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

As it could be a sensor related that acts up on that certain condition.
Many auto parts store has scanners that can be used to read transmission trouble codes.

Please let me know of any questions.
Thank you.

Yes, the car idles or kind of feels like it jerks or shakes a little, then it jerks again when it shifts into next gear. I just don't like having to worry about it when I drive around town, wondering if it will stall out or quit completely. Should I take it to a shop to get the codes scanned and hopefully that will tell me the problem?

A good first step would be to scan for any codes. That can help with the diagnostics.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Also, it would be a good idea to make sure the transmission fluid is at the correct level and in good condition.

Oh, and also there's a kind of burnt smell that sometimes comes through the air vents to, and when I go fast or push the gas it starts idling and the engine light starts blinking but it quits after a few minutes.

Is the burnt smell like burnt fluid or burnt wire smell?
Any smoke when you get the smell?

Since you are getting the engine light, scanning that will help determining what is causing this.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

No smoke or nothing that I can see, just the idling and slow acceleration when I push the gas pedal. Kind of feels like it's not getting a steady or constant flow of gas to the engine to make it run smoothly. But I don't why it's idling like that and why the engine light blinks for time to time during driving around mode. And does it cost anything to get the codes scanned to find out the root of the problem or problems.

You can take the vehicle to your local auto parts store, and they can scan and retrieve the code(s) for you free of charge. Typically, all the AutoZone, Napa, Oreilly's etc., have scanners available to use.
Let me know what codes you are able to find.