To find the unit rate of flowers per vase, you need to divide the total number of flowers by the total 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 answer is 8 flowers per vase.