After picking your flowers you can leave them sitting out without water for a couple of hours. They will get thirsty and once you cut the stems and put them in your dye solution they will absorb the color pretty quick.
You can create very dark flowers by using dark blooms to start; red flowers dipped in purple dye will end up a dark plum color, for example.
Put the flowers in a warm, dry room to help them dry faster.
Avoid flowers that are damaged or discolored, as this will still show even when dyed.