Yes, both genes combined will produce white males, on the females is different because they only have one copy of the barring gene.Maybe this is untrue and I was just misunderstanding what you were saying. But if this is true, then I don't understand the genetics behind that. In your last post, are you saying the barring and mottling combined produce a white male?
Barring while straight forward(Homozygous males are much lighter than Hemizygous females/Heterozygous males) one can take the regular barring gene mutation and breed for even lighter or darker birds(as the case with light barred Plymouth Rocks from Australia),
There are also four 3 sex-linked barring mutations, Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5384658/
Excerpt from the source: "We propose that the Sex-linked barring locus is composed of four alleles with distinct phenotypic effects: N, wild-type; B0, Sex-linked extreme dilution; B1, Sex-linked barring; and B2, Sex-linked dilution."
b+: Wildtype non-barred(b+/b+)
B0: Sex-linked extreme dilution(exceptionally rare, B^e/B^e)
B1: Sex-linked Barring(B/B)
B2: Sex-linked Dilution(B^d/B^d)
In the case of the 55 Flowery phenotype chances are that another mutation besides B1 is acting up on the males, but further research is required.
Old picture of Martin Silverudd main stock