How to use nonstandard audio sample rate data with audio DAC?
I only briefly looked at the datasheet.  This chip has a clock input called MCLK.  Again, I didn't read the details, but it certainly appears to be synchronous to that clock.  You should be able to get the chip to work over a wide range of sample rates by varying the clock.  There also appears to be some choice of scaling internal to the chip for a given clock.

Surely the details of that are to be found in the datasheet if you read it carefully.