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I read that oxygen makes up 21% of the Earth's atmosphere. I'm guessing it would take a lot of burning to decrease that level, but I am not sure how to calculate that.

The problem is: Roughly 400 hundred years in the future, humans are thinking they need to burn some forests made predominantly of a plant species that produces a gas toxic to humans and other life-forms, that spread on Earth and suffocated a lot of other useful (for us) plant species. They were worried that the large-scale fires would lower the amount of oxygen in the atmosphere to a level that humans would suffocate, but I can tell from the existing answer, that’s not going to be a problem, so they can go ahead with the plan.

I got the 19.5% threshold from this article: https://sciencing.com/minimum-oxygen-concentration-human-breathing-15546.html
But on a closer reading, I noticed it said the OPTIMAL range is between 19.5% and 23.5%, and the CRITICAL threshold for survival is 6%, so my mistake. Again, this makes the worries of the people in my story unfounded.
My question has been answered, thank you!

Let's start with considering the entire mass of the atmosphere:

The total mean mass of the atmosphere is $5.1480 cdot 10^18 kg$.

We know that Oxygen accounts for 21% in volume, and considering that

The density of air at sea level is about $1.2 kg/m^3$

We get that the "sea level" volume of the entire atmosphere is

$V =$$ 5.1480 cdot 10^18 over 1.2$$=4.29 cdot 10^18 m^3$.

You want to consume 1.5% of that volume (21 - 19.5), thus you want to consume

$M_O_2=4.29 cdot10^18 [m^3]cdot 0.015 cdot 1.429 $$ [kgover m^3]$$= 9.19 cdot 10^16 kg$ of Oxygen, considering that Oxygen density is $1.429 $$ [kgover m^3]$.

Assuming you want to burn Carbon to consume all that Oxygen, how much Carbon would you need?

The chemical reaction for Carbon oxidation is

$C + O_2 = CO_2 + heat$

therefore for each mole of Oxygen you need a mole of Carbon. Considering that Oxygen to Carbon atomic weight ratio is 32/12, you would need

$M_C = M_O_2 cdot $$12 over 32$ $=9.19 cdot 10^16 cdot $$12over 32$$=3.5 cdot 10^16 kg$ of Carbon.

The 2011 estimated coal reserves in the entire world amount to $891 cdot 10^12 kg$, just to give you a reference.

As additional note, burning that much carbon would release (taking the heat of combustion of anthracite)

$Heat = 32 [MJ/kg] cdot 891 cdot 10^12 [kg] = 28.5 cdot 10^15 MJ$, corresponding to about $6.7 cdot 10^6 MTon$, or about 1 million Tsar bombs...