Percentage of Oxgen left after burning all the available biomass
Estimates of earth's total biomass vary widely, from 0.5 to 4 trillion tons C, so instead of citing a source, I'll just go with an assumption of $1\times10^{15} \text{kg C}$. Measuring biomass in carbon is a convenient segue to the next assumption: assume that all biomass burns only in $\text{CX + O}_2\,\rightarrow\,\text{CO}_2 + \text{X}$.

Given these assumptions, $1\times10^{15} \text{kg C}\cdot \frac{1 \text{mol C}}{0.012 \text{kg C}} = 8.3 \times10^{16} \text{mol C}$. To react with so many mol's $\text{C}$ we will need the same number of mols of $\text{O}_2$, at molar mass $0.032 \text{kg O}_2$, which gives us a total of $2.7\times10^{15} \text{kg O}_2$ needed.

Oxygen is 20% of the atmosphere, which means there is $5.1\times10^{18} \text{kg atm} \cdot 0.2 \frac{\text{O}_2}{\text{atm}} = 1.0 \times 10^{18} \text{kg O}_2$ available. 

Since we have calculated that there are three orders of magnitude as much oxygen available as is needed to burn all biomass, I feel confident saying that global loss of oxygen due to burning biomass was not a cause of the P-Tr extinction. 

Also relevant: there is nowhere near a consensus that an asteroid impact caused the P-Tr extinction. To the best of my knowledge, an asteroid strike is not the most popular theory for that specific extinction event.