In response. No.
Baking soda does nothing to dry skin. There are several conditions that result in itchy dry knees: (1) One scrapes the knee and there is a scab forming on the knee. Because it is a scrape, the skin will form a scab. When skin forms a scab, it tends to itch. (2) The skin of the knees is dry, and it feels rough and powdery. The color is greyish. That indicates the presence of tinea corporis on the skin of the knee.
In both cases, use rubbing alcohol and hydrogen peroxide. Disinfect the dry skin of the knees with alcohol and hydrogen peroxide. If there is a fresh scab, let the scab dry out and harden. Make sure the scab dries out. Help the scab dry out by washing it with alcohol and hydrogen peroxide. A scab infected with tinea corporis or bacteria will not dry out and heal quickly.
Vinegar, alcohol, hydrogen peroxide as well as some Chinese rubs like Tiger Balm and White flower Oil can all stop the itch.