Not turning work

When my shawl pattern says knit row then do not turn and begin next row, how do I do this.?

What pattern are you following? Can you give us the name or a link to it?
As a guess, it might be something like an I-cord particularly if the row is 3-5sts or so. In that case you keep starting the row as stitch one without turning.

It is the blue sky window silk wrap. Thank you.

https://blueskyfibers.com/product/windom-silk-wrap/
It may be that you leave a yarn tail and knit across the row leaving a long tail at the end of the row for the fringe. Then you start again at the beginning of the row with a new strand of yarn.
So rather than tuning to the back you are always working across the front of the wrap.