To find out how many flowers Lindsay can water, we need to convert the capacity of her watering can from quarts to pints, since she uses 1 pint of water per flower.
1 quart is equal to 2 pints. Therefore, to convert 12 quarts to pints:
\[ 12 \text{ quarts} \times 2 \text{ pints/quart} = 24 \text{ pints} \]
Now, since she uses 1 pint of water for each flower, the number of flowers she can water is equal to the total amount of water in pints:
\[ 24 \text{ pints} = 24 \text{ flowers} \]
Thus, Lindsay can water
\[ \underline{24} \text{ flowers} \]