This is a whimsical neologism that builds off the first term (anti-dandruff). The logic is this: the shampoo is anti-X, but pro-Y: it is against one thing (dandruff), but for something else (beautiful hair that you can swish around).

Swishing your hair means tossing your head gracefully to make your hair fly out and look beautiful. Doing that makes a swishing sound (your hair rubbing against itself and/or the collar of your shirt/jacket), hence the word "swish" (chuinter).

A literal translation sounds bizarre in French, so we need an alternative. The connotation of swishing your hair is that it is beautiful and moves gracefully. Hence, "pro-souplesse" (since in FR, "souplesse" is a positive quality attributed to beautiful hair that moves gracefully).