How do I fix a Samsung UN40H5203AFXZA LED that TV flashes when I plug it in.

Take the TV apart and inspect all of the circuit boards, looking for bad electrolytic capacitors. When these go bad they often swell up and bulge. These are easy to replace if you know how to solder.
If the boards look good you need some experienced help, unless you want to start changing boards, hoping to find the right one.

These blinks [flashes] are fault indication (Error Codes). From the number of blinks occur at one time switch ON, you can get an idea about the faulty circuit section inside it. This will make repair easy. These are called blinking codes. Make sure about the exact number of blinking of the standby/power LED, by switching On & OFF the set, for at least two times. Count it carefully. If you wish to get some details, check the site linked here. It has details about blinking codes, and fault locating procedure, to many popular brand TVs and other devices.
http://electro-medical.blogspot.com/
http://electronicshelponline.blogspot.com/
If blinks continue without any pause, the main board is faulty.
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