To find the unit rate of flowers per vase, divide the total number of flowers by the number of vases:
\[ \text{Unit rate} = \frac{\text{Total flowers}}{\text{Total vases}} = \frac{112 \text{ flowers}}{14 \text{ vases}} = 8 \text{ flowers per vase} \]
Therefore, the unit rate is 8 flowers per vase.