I've cast my own rose gold, but used a rose gold master alloy (from Stuller if I recall correctly). A master alloy is basically everything but the gold, so for 14K rose gold you'd use 14 parts gold (by weight) to 10 parts master alloy. Especially if you're dealing with smaller quantities, it's just simpler to use the master alloys. They also tend to contain other additives, like grain refiners and deoxidizers, that will make your life easier. If you go that route, be sure to get a 'rolling alloy' for fabrication and not a casting alloy--it'll produce a more malleable product, whereas the main requirement for casting alloys is that they resist oxidization.
Similar to what Dave said, I'd first alloy the metals and shot the product (pour it into water) to make sure it's well mixed on the second go. Then melt your shot and pour it either into a sheet mold or even on a smooth, flat surface to get a flat "cast". Personally, I'd hammer it thinner before I even bothered putting it through the roller mill.
I just used a hand torch (acetylene/air) when I did mine. Note that some master alloys are formulated for different types of melting, too--open air, torch, induction, etc.
You will want to re-anneal your gold quite often. You'll feel it stiffen up after a few passes through the mill--that's when it's time to anneal again. If you dip your piece in boric acid before annealing, it'll resist oxidization and won't need to spend as much time in the pickle pot.
Final note: Red gold refers specifically to karated gold that only uses copper as the non-gold metal component. Rose and pink gold can contain other metals. For example, 18K red gold is very brittle, so 18K rose gold actually contains a bit of silver to soften the alloy.