Since fire require oxygen, wouldn't a fire, like those in the American forest along west coast, constantly draws in oxygen from around? And if that is so, would the concentration of oxygen around the fire higher than farther away?
A fire has no way to directly "draw in" oxygen for it to burn. It consumes what oxygen is in the immediate vicinity of the flame, depleting the air in oxygen compared to the concentration of oxygen in air further away. This sets up a concentration gradient such that oxygen will diffuse into the depleted region near the fire.
An even more important process than diffusion of oxygen into depleted air is convection driven by the heat of the fire. Oxygen-poor air that has been in the fire gets hot and rises, drawing fresh air into the base of the fire. Note that this still isn't oxygen being drawn to the fire, but a mass of fresh air flowing into the lower pressure area at the fire resulting from convection.
The bottom line is that a fire consumes oxygen, so the region around the fire will be slightly depleted in oxygen, not enriched as you suggest.
Since fire require oxygen, wouldn't a fire, like those in the American forest along west coast, constantly draws in oxygen from around?
That doesn't make sense. You are reversing cause and effect; you are saying that since the presence of oxygen (along with other factors) causes fires, that this somehow mean that fires will cause the presence of oxygen. That would be like saying that putting solar panels on your roof causes your roof to get more sunlight.
No, it'd be more like the water level around a drain.
Sure the presence of a drain causes the water to flow in that direction, but the water flows in that direction specifically because that region's still water-deficient despite water flowing to it:
Same deal with the fire and oxygen. Oxygen's net flow rate will tend to be toward the fire, but it'll be toward the fire because that area's oxygen-deficient, i.e. lower oxygen levels. If the fire for any reason stopped having lower oxygen levels, oxygen'd stop having a net positive flow toward it.
Phenomena like this are often modeled with Fick's laws of diffusion. Typically, the result looks like the concentration profile of the diffusing species (in this case, oxygen) decreasing from some bulk concentration (in this case, atmospheric concentration) to the concentration at the sink (in this case, the fire's vicinity).
In the above, if the oxygen concentration around the fire $C_1$ were to become higher than the atmospheric oxygen concentration $C_0$, then oxygen would start flowing away from the fire.