The way you make a HUD is not with a flexible display (this would be complicated and expensive).

Instead, you put a semi-reflective coating on the glass. Stickers are sold for this for automotive use (https://www.amazon.com/Reflective-Windshield-5-9x5-1inch-Windscreen-Protective/dp/B09LYLD59N).

Then you use a high brightness screen pointed at that reflective surface. The display should be inverted horizontally (...because text is backward in a mirror, right?). What you see as the 'HUD' is actually the reflection of the screen. This is how automobile manufacturers do it. They look pretty OK.