If you are primarily interested in keeping the fire from begin seen, you could dig a hole and build a small fire in the hole. That, plus maybe the dirt from the hole piled up around the hole, would contain most of the light shining out to the sides. There would still be the light shining upwards, so you'd want to be careful about what is nearby or overhead that could reflect the light. This would include the skin and clothing of anyone around the fire.

Having your fire in a hole or pit also has the advantages of reducing the wind blowing on the fire, and it contains the fire so you don't have the concerns about the fire getting out of control.

When you break camp, you just extinguish your fire and fill in the hole. If the fire has not been allowed to burn itself out, and your fire pit was not dug in sand or rock, be sure to put the fire out THOROUGHLY before burying it. You wouldn't want something underground to smolder and spread somewhere and start a fire.

If you are going to want to disguise the pit after it's filled in, you might consider digging it in a place where you can move and then replace natural features such as rocks and logs. After filling the pit, put the rocks back as they were when you got there. Use your imagination. You might also want to read an Army survival manual. I have a 1970 edition of FM21-76, and it is excellent.

Smoke can give you away, even if the smell does not. Be sure to use really dry wood and add it slowly.