Thank you for giving the full context. "She was repelled by those lacerated hands, grimed by toil so that the very dirt of life was ingrained in the flesh itself, by that red chafe of the collar and those bulging muscles..." hey, is that from Jack London's _Martin Eden?_ (Checking) It is!
"The dirt of life" is not an idiom or a standard expression.
I believe "the dirt of life" means that, as a sailor, constantly doing hard labor with his hands, he was handling dirty things. "The dirt of life" means "the dirt he encounters in his daily occupation." His hands always look dirty. The dirt can't be washed off. It is "ingrained," embedded, has become part of the flesh itself.
I love that book! It is obviously based on Jack London's own life. It is NOT in easy English. Good luck, I hope you are able to read it with enjoyment.