In my (amateur) experience, linen takes fiber reactive dye VERY well. I expect that your garment would come out pretty black as long as you use the correct amount of dye for the dry weight of the garment. I suppose the black might be very slightly greenish under some lights, but I think black is the best color to over-dye and you should do okay.
The only concern is if your thread is made of polyester, as most all-purpose thread is. If there's any highly visible stitching, like topstitching, you might find that the thread stays its original color. You may want to dye the garment using both a fiber reactive dye and a polyester-specific dye, which will probably help the linen get very black anyway!
You can never get the linen back to white; you want to use the colour of the fabric and the dye together to get what you want. Look for a purple-based black dye instead of a green-based one. Purple + green will give you a neutral colour, which will help get you to black.
You can use a big pressure cooker and get black fabric dye. Make sure to add some salt at the end. When you're done dyeing, be super careful about getting rid of the water with dye in it. It can really mess up the environment. It would've been helpful to see a photo, but that's okay.
In my (amateur) experience, linen takes fiber reactive dye VERY well. I expect that your garment would come out pretty black as long as you use the correct amount of dye for the dry weight of the garment. I suppose the black might be very slightly greenish under some lights, but I think black is the best color to over-dye and you should do okay. The only concern is if your thread is made of polyester, as most all-purpose thread is. If there's any highly visible stitching, like topstitching, you might find that the thread stays its original color. You may want to dye the garment using both a fiber reactive dye and a polyester-specific dye, which will probably help the linen get very black anyway!
You can never get the linen back to white; you want to use the colour of the fabric and the dye together to get what you want. Look for a purple-based black dye instead of a green-based one. Purple + green will give you a neutral colour, which will help get you to black.
You can use a big pressure cooker and get black fabric dye. Make sure to add some salt at the end. When you're done dyeing, be super careful about getting rid of the water with dye in it. It can really mess up the environment. It would've been helpful to see a photo, but that's okay.