How to calculate air flow from a pressurized tank?

The most simple way is to model your pneumatic system as an electrical circuit analogy. This approach can get you close to the true physical behavior as long as you don't have thermal effects due to gas flow and if you are able to 'lump' a continuum of parameters as a single parameter.

In the pneumatic-electrical circuit analogy volumes provide a compliant space for the has to compress and expand, and so volume can be expressed analogous to capacitance. And the orifice through which the gas flows is analogous to electrical resistance. Flow is analogous to the electrical current, and pressure to voltage.

You didn't show a diagram of your specific problem, but that's where you would start. And from that diagram you would draw the electrical circuit analogy. Start with a linear circuit- linear resistance and compliance. But you find that for resistance a quadratic relationship better models the component of flow resistance: $Delta P=Q^2R$. You'll find this to be a close approximation to the orifice equations you researched. The pressure due to compliance is $P= frac{1}{C} int Q dt$. And compliance is $C= frac{V}{P_a}$ where $V$ is the volume of the space you are considering to be the compliance, and $P_a$ is the absolute barometric pressure. In an electrical circuit there is 'ground' voltage and in the analogy that's barometric pressure which can be taken as zero by using gauge pressures.

For air, when the downstream absolute pressure is 52.8% or less of the upstream absolute pressure, the flow is choked (limited by the sonic velocity, mass flow rate independent of the sink pressure). Your comment above says the source pressure is about 130 psi, so depending on the hose (sink) pressure the flow may very well be choked.

You can find relationships for choked (and non-choked) flow in textbooks and articles on fluid flow. For example, see articles on the web, or a text that discusses fluid flow, such as Elements of Thermodynamics and Heat Transfer by Obert and Young, or Flow of Fluids through Valves, Fittings, and Pipe, Crane Technical Paper 410. The Crane reference provides equations, and graphs of discharge coefficients and other parameters in the equations.