A coat of
A coat of fiberglass polish will help. Worst case scenario is you bring the chair to an auto-body shop and have them do a semi-gloss clearcoat on the whole chair.
Color
How did they do the color originally? Was it in the fiberglass resin or did they mold them and then paint them? I wonder if when filling big gouges if it's better to put the color in the epoxy or to just fill it then paint and clearcoat it?
Both
There were some chairs that were painted, but the majority of them were colored in the resin. There's a wonderful Eames film about the making of the chairs. Fiberglass polish should minimize the whiteness of the scratches. What you most have to worry about is the glass fiber being exposed. Mucho itchy if it is. A clearcoat should trap any of the exposed fibers, and will also provide a bit of a barrier.
the way
fiberglass chairs are constructed by bonding a mess of glass fiber in a plastic resin. The resin is baked and solidifies giving the chair the form, while the glass fiber gives the chair its strength. When the chairs are pressed into a mould, the interior of the mould has been sprayed with a clear finish called a gel-coat. The gel-coat acts as a barrier - sort of like polyurethane on a wood.
Your scratches look deep enough that they may have gone through the gel coat and disturbed some of the glass fiber.
Quick and dirty solution: clear nail polish
DIY solution: spray on clear polyurethane
Long term solution: professional clear coat
Most instances I've heard of people DIY painting these things don't last very long. The paint peels and chips away fairly quickly because the gel-coat is naturally smooth. Also, painting obscures the swirls of fibers that give the fiberglass its organic character.
