anything that BREAKS water-tension will allow fleas to drown -
it also prevents them from leaping onto & off the water-surface, to escape the tub!
Fleas are so small, they can literally "walk on water" or more accurately, leap atop it w/o breaking the surface.
baking-soda, a mild bar-soap, any shampoo, etc - they all work, to 'make water wetter' & break the surface-tension.
I like to use organic shampoos that have no SLS
[sodium laureth &/or lauryl sulfate, & relatives], also no formaldehyde, chemical colors, fake fragrances, etc.
Coloring & perfumes cause lots of rashes. // The shampoo should also say "pH-balanced" on the label.