Plant the rose cuttings at any point throughout the year. Some people like to plant them during the cool months, while others wait until the early summer. Rose cuttings should be able to grow during any season. However, keep in mind that they'll need to be constantly watered, so if you plant them during the summer or live in a hot climate, they're going to dry out faster. For this reason, the rainy season might be your best option.
I too, have tried the cut rose flower method, but haven't yet been successful--perhaps because there are chemical additives that the roses have soaked up, or because there are no nodes (which are the points where new shoots grow out), or because the stems have spent much of their energy producing the flowers...BUT, perhaps if the flowers were immediately cut off and some rooting hormones applied to the bottom cut ends, that may work.
I planted mine in to the ground just like a normal rose bush, amending the soil with rose fertilizer and alfalfa meal. It is gorgeous, but because it's low to the ground, you should make sure to use drip irrigation or a soaker hose to water it so it doesn’t get black spots from the water splashing on the leaves. If yours is in a pot, let it go dormant in the garage or close to your home to keep the pot from freezing. Keep it watered and in the spring it should come back with more fertilizer to keep it happy.