Too late to edit the above post, sorry.
The first time I viewed your post, the closeup showing the smaller flower didn't load, so I couldn't see it.
The flower is made of a bias-woven tape, which is gathered to make the flower and sewn in place. This is less typical of Battenburg, but it's still the same basic type of lace. I'm afraid I am drawing a blank on whether there is another generic name for this, or a more specific name.
The ring in the center is called a couronne, IIRC. It's often used in needle-lace, and Battenburg does use needle-lace stitches to join the different kinds of tapes that were used.
It's a well-made piece, at a guess, early to mid 20th century based on the condition. Since the ground is a net, it's possible that this was intended as a decorative coverlet, rather than a tablecloth. The net, and the 3-dimensional decoration, would be less practical as a tablecloth.
