Is $\mathbb{F}_p$ flat over $\mathbb{Z}[1/N]$ ($N\geq 5$, not divisible by $p$)?

Question

I am trying to understand the paper "Generators and relations of the graded algebra of modular forms", N. Rustom. It is being claimed that for an integer $N\geq 5$ and a prime $p$ not dividing $N$, $\mathbb{F}_p$ is flat over $\mathbb{Z}[1/N]$. In what sense should this be understood? I think that for a PID (such as $\mathbb{Z}[1/N]$) the quotient by a maximal ideal can not be a flat module.