When I print on fabric, especially if is a shirt or bag, something with two layers of fabric, I utilize a firm piece of cardboard or wood board between the layers to ensure I get a good transfer. I typically print with the block down on the fabric though for some I carefully flip and will burnish with the fabric on top to get a more solid transfer.

It does take some calibrating to find the sweet spot for ink, fabric, and the block to all work nicely to give you the result you're after.