My experience is that beeswax has a dull sheen, but can be buffed. For chairs, you might want to use something that polymerizes, or at least hardens. Beeswax alone softens with heat, and can liquify if exposed to the sun.
Bees wax and linseed oil will provide very limited long term protection. Fine Woodworking did an article on oil and wax finishes many years ago. These finishes are fragile and require care. No, they were not used on violins.
I use a 1:1:1 Linseed Oil, Turps, Beeswax mixture to periodically recondition interior furniture. It brings out color and sets up to a dull sheen but it doesn't go deep and remains soft. Like the man said, very fragile.
OTOH, 1:1 Oil and Turps is lovingly referred to as "boat juice" and I slather it on every part after gluing but before nailing and at the beginning and end of every season.