I've never heard all to the silk, but it must mean "on the level", don't you think?
A silk, in BrE, is a high status lawyer, or Queen's Council, but I don't think that helps. Perhaps Chandler had in mind the expression 'pure as silk'. Or perhaps he just heard someone say 'all to the silk': I know he kept notebooks full of colloquialisms and things he'd overheard.
I searched for an hour or so online last night for a book that ought to exist. It would be called "Decoding Chandler" or something like that. It doesn't seem to exist yet but someone should write it before his language slips through our fingers along with the clothes, perfumes and gadgets he mentions that are no longer around.
I happened to be three-quarters of the way through The Big Sleep but when - looking for an answer to your question - I found Goldfish online, I downloaded it, poured a glass of whisky and read it. So thank you. Good story.