A bit about the Genetics regarding Coat Colour:

A Chocolate dog (like "Lets Duck and Run") can only be one of the following two types: bbEE (Chocolate), or bbEe (Chocolate, carrying Cream)
A Cream dog with a black nose (like Flossy) can only be one of the following two types: BBee (Cream, carrying Black) or Bbee (Cream, carrying Black and Chocolate)
Regarding the Genetics of Coat Colour (the two best websites I could find were Astrochoc and VetGen) so if you get as lost as I did, please refer back to these two rather excellent and layman-proof websites...
Black is a dominant gene. A Black dog may carry other genes namely Chocolate (the labrador name), brown (the same colour but the poodle name) or Yellow (Lab name) or Cream (Poodle name). Yellow and Cream is basically the absence of black or brown - so it means all variations from white to apricot (poodles) or yellow to russet (labs). The B denotes the dominant black gene and the b denotes the "absence of black" recessive gene.A black dog must also carry the E genotype, meaning he can display a dark coat. The 'e' genotype means he can't display a dark coat. If you can't see it but they have got it, its recessive (I think). Complicated isn't it? !!
As Flossy's last litter contained only black and chocolate puppies one could therefore safely assume that she is Bbee and Lets Duck and Run is bbEE.