How to deal with clear flakes off my wooden headboard
Clear flakes are probably some type of varnish.

I would sand the surface to remove the loose flakes and to make the surface as flat as possible, then refinish with a similar varnish. I would follow the instructions on the container very carefully. Preparation is important for a good result. You can buy tack-cloths to remove dust before applying varnish.

Usually it is best to use the same type of product as was used originally unless you sand the whole thing back to bare wood. It can be hard to identify exactly what type of product has been used. I would start by experimenting with new finish on a small area that isn't usually seen (e.g. the back of the headboard)

In an apartment, if I had no access to the outside or a balcony, I would take the headboard to a room that has good ventilation and where dust can be cleaned up easily. Maybe a utility room with a window that can be opened? I would use a well-fitting disposable dust-mask when sanding. I would try to avoid spending long periods in the room when sanding or applying varnish.

Editing the question to include a good photo might help readers identify the flakes and suggest other remedial actions.