What are the dangers of Linseed Oil fumes?

You need to find out if the linseed oil is RAW linseed oil or BOILED linseed oil. Linseed oil is oil squeezed from the flax seed. 

Raw Linseed Oil is 100% pure flax oil, packaged with no additional additives or preservatives. Linseed oil sold for wood application is not edible. It dries very slowly, taking weeks to fully cure. It helps wood retain its natural moisture content, which reduces cracking, checking, shrinking, and aids water repellency. 

Boiled Linseed Oil contains chemical solvents to speed film drying and hardness. 
It is not actually boiled, the term just indicates chemicals have been added. 

Do ask the dealer. Boiled Linseed Oil would cure faster and shouldn't have an odor after several weeks. If it's raw linseed oil, it's likely you are smelling the linseed oil itself, which isn't toxic.

Debra :-)

This answer was provided by our friend, Debra Lynn Dadd. Hailed as "The Queen of Green" by the New York Times, Debra Lynn Dadd has been a pioneering consumer advocate since 1982, specializing in products and lifestyle choices that are safer for human health and the environment. She is the author of Home Safe Home.