Well, here's what I've come up with.  I ended up with two ideas. The first is a more traditional business card; screen printed in one color on front and back, with the flower on the back debossed, to go with my leatherworking (alternatively, I would use a stamp and thermographic powder to achieve an embossed effect).  This would be a very heavy paper, #170, in chocolate brown (the paper lost some of its brown-ness in the conversion from CMYK to RGB). I'd also like to do edge coloring with the red of the brand color palette.

Red:

Front:

Back:

The other idea that I came up with is of the more useful idea; an actual leather business card that could be used as a bookmark, using a custom made leather stamp and press, with die cut pieces of thin leather.  These would be stiff enough due to the finish I would apply to slip into a wallet. I used Photoshop to show what this would look like (at least sorta).

I'm fairly excited about both ideas and I'm going to have a hard time picking between them!