Magnetic Flux

Magnetic flux is the field weighted by the area it passes through and by orientation: $\Phi_B = BA\cos\theta$ for a uniform field over a flat loop, with $\theta$ measured between $\vec{B}$ and the loop's normal, and $\Phi_B = \int \vec{B}\cdot d\vec{A}$ when the field varies across the surface. An $N$-turn coil links that flux $N$ times, so the quantity Faraday's law differentiates is $N\Phi_B$. Field, flux, and flux rate are three separate rungs, and only the third one induces anything.

Two errors dominate. Treating flux as a synonym for field, so the strongest field in the problem is assumed to carry the most flux and to induce the largest EMF, when a coil parked in a $1.5$ T bore induces zero. And dropping the bookkeeping: forgetting the factor of $N$ on a multi-turn coil, or measuring the angle to the loop's plane instead of its normal, which turns every cosine into a sine and reports maximum flux for the orientation that actually carries none.