Have searched in the Offical Records and found no mention of this unit or the officers you have listed except that the spelling of Captain Wilke was possibly first listed as Willke. The correction to Wilke is in the General Index, volume 130, (corrections to volume 4) listed on page 1108. A Capt. H. Willke of the Texas Provisional Army is mentioned in volume 4, page 167 as being at Fort Brown and conducting a survey of the condition and armament of the fort. The correct appears to have been made in the National Historical Society's edition. Have found nothing else. So your Captain may be spelled as Willke or Wilke. Hope this helps.
Ron