From what I have read you will be given the time by Disney Dining. It seems that for the Fantasmic Dinner package they have pretty early dinner slots available. If you are given various times when you call I would allow at least two hours so you can relax during your meal and still have plenty of time to get to the show.
Do you know if there are 2 Fantasmic shows that night? On our last trip, they had an early show (around 7ish) and a late show (around 9ish). The earlier show is usually much more crowded than the later one.
Another thing to consider is that Mama Melrose is on the opposite side of the park from the FDP entrance. So allow plenty of time to walk over from the restaurant.
We did the FDP at Mama Melrose 2 years ago, we arrived at the special entrance about 20 mins before the first show and were turned away because they'd already seated the FDP people 10 mins earlier and were now seating the standbys. At the time, I didn't realize we had to be there 30 mins early and hadn't taken into consideration how long it would take to walk across a very crowded park. They did tell us to come back for the second show and we sat with the FDP group.
Sorry I can't tell you an exact time that would be best, but be sure to allow plenty of time! Have a great trip!!
We made a 6:10 reservation for MM on the same night (July 11). The CM I spoke to on the phone said that would give us "plenty" of time to get to the show at 9:00 which is the first show that night.