How can I have a position: fixed; behaviour for a flexbox sized element?

You can't.

As explained by the CSS2.1 spec:

Absolutely positioned boxes are taken out of the normal flow.

And the Flexible Box Layout spec confirms that:

An absolutely-positioned child of a flex container does not participate in flex layout. However, it does participate in the reordering step (see order), which has an effect in their painting order.

^{(Emphasis mine)}

Here's a way to do this inspired by bootstrap:

.fixed-top {
  display: flex;
  position: fixed;
  top: 0;
  left: 0;
  right: 0;
}

This gives your flex-box room to breathe and do it's flex-box thing. If your flex-direction is column, you could use top, left, bottom instead.

This works because when you give an element a fixed position and a left and right of 0 or a top and bottom of 0, the element is stretched to fill the space from left to right, or top to bottom. That in turn allows a flex-box to use the amount of space you would expect without position fixed.