Ask Mr. Smarty Plants

The Lady Bird Wildflower Center Native Plant Database says the following about Bauhinia lunarioides:

Native only to a few canyons in western central Texas and in adjacent northeastern Mexico, Anacacho orchid tree is a 6-12 ft., single- or multi-trunked shrub or small tree with small, light green, deeply cleft leaves. Delicate white to pale pink, orchid-like flowers with extended stamens appear prolifically in clusters. Fruit is a flattened pod.

Anacacho orchid tree makes a gorgeous display with its silvery gray bark and fragrant white flowers that resemble orchids. It is a relatively rapid-growing tree after its first year when placed in a favorable location, but should be planted on the south side of buildings in areas with harsh winters. The nectar attracts butterflies and bees. 

Propagation Material: Seeds
Description: Untreated or acid-scarified seed planted in spring
Seed Collection: Collect in mid- to late summer when pods are brown and dry.
Seed Treatment: Scarification may help.

A search of the internet did not find any information about successfully starting Bauhinia lunarioides from cuttings, the bulk of the information was about propagation from seed. Other Bauhinia species though did have information about propagating by using root cuttings or stem cuttings.  

Here's what the Floridata.com website says about propagating B. variegata:

Propagation: Seeds germinate readily. Orchid tree also can be propagated from cuttings of semiripe wood taken in summer and rooted over bottom heat. Branches can be induced to grow roots if they are layered, either by burying a section in the ground, or scarring a small section and then wrapping it with damp sphagnum moss and enclosing in a plastic bag. The tree sometimes produces suckers which can be dug up and replanted.

Howard Garrett, the Dirt Doctor has some good information on his website www.dirtdoctor.com about Bauhinia lunarioides and says the following about propagation: 

Collect the seed pods in the summer when they have turned brown but before they open. Air dry the pods a few days, dust with natural diatomaceous earth and store in glass in a cool place if necessary. The seed can be planted without treatment outdoors the following spring after the last frost. Look for germination within 3 weeks and transfer the seedlings to 1 gallon containers when they have 4-6 true leaves.

The Aggie Horticulture website at TAMU has some additional information about propagating Bauhinia lunarioides and other species.

Seeds of this species germinate without pregermination treatment. However, other Bauhinia spp. seeds have physical dormancy and must often need scarification. Bauhinia variegata and B. xblakeana (evergreen tree with thick leaves and striking purplish red flowers) are also important Bauhinia plants. B. xblakeana is a sterile hybrid propagated by air layering. B. purpurea has been micropropagated.