Can I get a HD camera with FLAT lens?

I need it for recording my face from close. Normal cameras make my nose huge. I love my iphone camera but then, it is not HD.
What shall I look for? What are they called the ones with FLAT lens?

HD is a video term, not photography.

I have no idea what you mean by "flat lens".

The reason peoples faces/noses are distorted is because they have no clue how to use a camera.
If you take a photo with a wide angle lens (i.e. From the end of your outstretched arm), you will get distortions.

A real photographer uses a longer focal length, then those distortions won't happen. Those lenses are by no means "flat". Decent portraits are taken from a decent distance.

A bit of knowledge goes a LONG way.

Wide angle lenses tend to distort facial features, such as noses. Longer focal lengths, such as telephoto lenses tend to "flatten" facial features, which is probably where you got the idea.

In the camera world, lenses between 85mm and 100mm are "neutral" in the sense that anything wider starts to round objects, and anything longer tends to flatten objects. This is why 85mm is so popular for portraiture.

With smartphones, all lenses are wide angle, and you zoom in by cropping the photo. This means the "rounding" characteristic is there regardless of the zoom position.

You can mitigate this distortion somewhat by being more distant, so back up some when taking such photos. Your face will be smaller in the photo - but that is the limitation of not-so-smart phones.

There's no flat lens nor is there an HD picture. What makes your nose look bigger is the fact that you are shooting up close and probably with a wide angle lens. Shoot from a fair distance using a normal/standard to short telephoto lens to avoid distortion. Find the best angle to make your nose as normal as possible.