Rose's Flying Dress Costume consists of a white bodice with dark blue skirt, paired with a jacket with embroidered lapels. There are coordinating accessories in cream: a shawl, embroidered kid gloves, and a purse with a trio of tassels. She also wears this costume with vintage shoes and her infamous butterfly comb. There are some fantastic sites online that have already research the gowns from Titanic - check out the links included below.

Bodice - The lacey bodice is two layers: a white silk underlayer and a Chantilly or Alencon lace overlayer. Lace scallops frame the neckline. We don't know if the bodice is simply a 'tube' or actually has straps, as these are hidden by the jacket.

Skirt - There are two layers to the floor-length skirt, probably both made of silk satin. The top most layer is gathered slightly at hem on the left side, creating a drape. This exposes the underskirt, which is embroidered with a variety of blue flowers (much like the jacket lapels).

Jacket & Sash - The jacket looks like silk velvet, with silk satin accents on the cuffs, lapel, and collar. The sleeves are 3/4 length and feature cuffs made from three satin bands decorated with three buttons. The lapel (also in satin) is embroidered with flowers in varying shades of blue. The hem is curved, with tassels at each point created by the hem. The sash is also satin, with the gathers most likely tacked into place to keep their shape.

Linkage:
Maggie's Titanic Costume Research
J. Peterman Costume Collection - awesome reproductions inc. shoes and bag
Sense & Sensibility's Titanic Project