What are the best compression garments to wear for ab, flanks and back lipo?

You should use the garment that your surgeon recommends after liposuction of these areas. In the end however there's no evidence that compressive garments have any effect on the long-term outcome.

Compression Garments are typically a matter of surgeon experience and taste.  That said, when our patients have liposuction in the abdomen and flank area, we us a foam vest made by Marina.  It has several benefits.  First it keeps your abdomen and torso area upright decreasing the risk of pleating of your skin when healing.  It also evens out the pressure that is applied by the garment, which when applied unevenly, especially when skin tightening, superficial liposuction technique is used, can significantly increase the risks of post operative healing deformities.  Otherwise, most garments are fairly similar!

I usually suggest Marena or Veronique, but there are many good companies on line. Best to ask your surgeon.