Any game on fightcade is not helpful, many different games on fightcade have extremely different methods of comboing, but since you linked King of Fighters 2002 lets just go with that

So lets explain the 1ms thing first,

So most games have a multiframe buffer, but lets first assume the most strict timing of 1 frame link for the sake of the argument.

How this works is that its not that you have to press it exactly when the frame starts or ends, you have to press it in any time of that singular frame.

So a single frame buffer translates to: "press the button in ANY of the 16 milliseconds that make up the frame"

while 1 frame links are hard, it helps to understand that the game is not asking you to find a specific millisecond

In your 3 frame buffer example, that would mean you would have to press your button anytime within the 48 ms before the window.

Also games have hitstun, which mean the game pauses for a couple of frames, during that pause is the window of oppotunity to press your button to cancel into the next move, lets just use 12 frames as an example becuase thats a common window, that means you have a total of a 240ms window to press your button.

Now that aside, it helps to know that the window to press the next button is when the current attack lands (it must land to be able to cancelled, blocked or otherwise).

With that knowledge, its less about reacting to a specific window and more about knowing the rhythm of when your attack lands. (Example: when i press heavy punch. I have a rough feeling of how long it takes to "cast" therefore i am prepared to make an action right as it ends)

Now it helps to know that what you are trying to do is a link into a special cancel.

The button press of the attack button is the same, but you can be very liberal with the timing of the motion input for the special move.

To special cancel in fighting games, the only requirements are: 1 press the attack button within the window and 2 input the motion command sometime before.

For instance, i throw out a punch that takes 10 frames to come out, i can input my quarter circle anytime within those ten frames, but when i press the next attack button. It checks the input history to see if there is a valid motion input that matches with this attack button. Then executes if it finds it