I applied linseed oil to a hardwood floor.
Instead of using pure linseed oil, which may have been a better idea, I used a butchers blocks liquid from IKEA called Behandla made of linseed oil, a drier and a plant-based emulsifier.
It gave a slightly wet/dirty look to the floor that does not seem to disappear after some days.

https://photos.app.goo.gl/EVsBwGLPoQbYGHL87

https://photos.app.goo.gl/uhJ4nvYbqpdP7uPE9

Before sanding and restarting with linseed oil, I was wondering if any easier method would allow to make this floor look more homogeneous with less dark wood veins and so on.

Thanks

Linseed oil takes a very long time to harden. It gives a look like oil based finishes and darkens over time. You may be happier with a water-based poly-urethane if you like light colored floors. I would let it dry for a week or so then buff with #2 steel wool, shellac and coat with a water-based poly.
Test an out of the way area to see if you can get good adhesion.
If you want a lighter floor you will need to sand to bare wood.