I don't think there is any single answer to this question, because it would depend on:
- The type and thickness of the steak
- The starting temperature of the steak
- How well you like it done (because the goal is to get enough browning and crust development on the outside, without crossing over into burning, while still cooking the steak through)
- The peculiarities of your own equipment, including both your element and your pan (a thick heat retaining pan will have less temperature drop than a thin one, and so require less ongoing source of heat)
Even if we could give you a single answer, it would probably be in terms of the surface temperature of the pan before you put a steak into it, and unless you have an infrared thermometer (which have only become reasonably available in the last 10 years or so, and are not typical kitchen equipment), that answer would not be actionable to you.
So we fall back on less precise methods, saying things like the oil should just be smoking, or that it should be shimmering, or that a bread cube should brown in about 5 seconds.
Perhaps the best test also requires the most experience to apply. Hold your hand, open, palm down, over the surface of the pan about 1 inch (2.5 cm) from the surface for a few seconds. The length of time it takes for it to become uncomfortable tells you hot how the pan is. It should be about 3-4 seconds, but again, requires experience to use this method, and everyone's perception varies.
In any case, you are going to have to employ trial and error as you learn the idiosncracies of your own burner, and your own taste in steak.
That said, there are a couple of methods that are more forgiving. Possibly the best is cooking sous-vide, and only searing for browning afterwards in the pan, but not everyone has the equipment and wherewithal of that method.
A technique that anyone can do is to put the steak in a slow oven (about 250 F 120 C) until it is cooked through about 5 degrees F (2-3 C) below the doneness you like, as tested with an instant read thermometer. IT will be wan and pale looking but this is okay. You then sear it in a quite hot pan, until it is brown and delicious. This should only take a couple of minutes, since the steak is cooked through; you are just developing the crust. This shorter time should be much less likely to burn.
Note: within limits, a thicker steak requires a lower temperature, but this is very limited.
Thick steaks truly require a two-stage cooking method, such as the ones outlined above, or traditional pan roasting (searing in the frying pan, then transferring to the oven).
In the end, though you will always have to come back to experience with your equipment, and your preferences on how you do your steaks.
(1) It is worth noting that many people prefer stainless steel pans to cook meats on because they are NOT non-stick (meaning they stick). The fat rendered during cooking, along with the bits of fat and meat that stick to the surface are called "fond" and are used to make pan sauces to serve with the meat. This is a big selling point for SS pans.
(2) Polishing the surface of your pans to a mirror-finish won't make your pans non-stick. The sticking has more to do with the properties of the stainless steel itself rather than with the buffing of the surface. Some people have suggested that you can season a SS pan like you can a cast-iron pan to make the surface non-stick but that sounds fishy (but, admittedly, I have never actually tried that - I used different types of pans for different types of cooking).
(3) Some seasonings just burn very easily - like paprika. Seasonings that burn easily will most likely burn or scorch whether they are still on your meat, or if they have strayed to the pan. Any spices that might burn should be applied shortly before the meat finishes cooking or applied when you serve it.
Best Answer
The best way, imho, is to use your basic broiling pan...Put a little water in the bottom before you start, or the pan may warp. Put the rack in your oven as high as it will go (while still allowing the broiling pan with steak to fit), then turn the oven on "Broil".
Leave the oven door cracked (you don't want it to pre-heat, and turn the element off), and cook it like you would on the grill, flipping it halfway through. The radiant heat from the element will give you a little char, though no grill lines, obviously.
Anything over medium rare is going to be a bit chewy. Let it rest, then cut it into strips across the grain of the meat. Flank steak responds well to marinades (my favourite: 1 tbps soy sauce, 1 tbsp sherry, 1 tbsp dijon mustard, 1 tbsp lemon juice, 1 tsp ground ginger.)
You could try to cook it on the stovetop, but that much meat will be too much for most pans.