Meat birds do not breed true so it won't work. Every hatchery has their own mix of breeds so if you like one they have you can go on their website and find out what breed they use for both the male and female. Then when they breed the chicks will be broilers. This is from cacklehatchery.com:
"The Cornish Cross Chicken (Cornish X), (Broiler), (Cornish/rock), (Jumbo Cornish cross) is a cross between the Commercial Cornish chicken and a White Rock Chicken." ..... "Cackle Hatchery currently hatches out the “Cobb 500” blood line/strain with occasionally hatching the “Ross 308” blood line/strain."....
Some places specify what one should be the hen and what one should be the roo to get the mix they have. Every place has a different mix they use but some of the most common are leghorn, white rock, and regular cornish. It may take a while and some trial and error to hatch out your own but it is possible.