Mate, it's not linen. I've had this before with "too cheap to be true" "linen" articles from China. It's not linen and it won't dye.
The OP has said that the jumpsuit in her link is not the one she owns - just an illustration of the colour.
But if yours is a similar price, @user1471867483, or if any part of it is synthetic (such as the stitching mentioned above) it’s not going to be worth the cost of dye. You almost certainly won’t get the result you hope for.
And anyway - you obviously like the original colour. Maybe time to grow a backbone? That couldn’t fail to be stylish.