Flagstone Patio Prices: The cost of a flagstone patio varies widely depending on your location, the amount of flagstone needed, as well as the type and color of flagstone. You can expect to pay between $15 and $30 dollars per square foot.lagstone Patio Prices: The cost of a flagstone patio varies widely depending on your location, the amount of flagstone needed, as well as the type and color of flagstone. You can expect to pay between $15 and $30 dollars per square foot.