I checked out your webpage and was intrigued with the flag depicted at the top of the page, five stripes, red, white, red, white, red.
It seems quite unique. If of the Civil War era and associated with the company, I would suggest you share your find with the Flag Message board.
For information, I checked out the Carlisle Barracks unit bibliographies and came up with the following, in case you may not have already found it.
Good hunting,
George Martin
U.S. Army Military History Institute
Historical Services Division
950 Soldiers Drive
Carlisle Barracks, PA 17013-5021
19 May 06
Oneida Company New York Cavalry Regiment
Dyer, Frederick H. A Compendium of the War of the Rebellion. Vol. 2. Dayton, OH: Morningside, 1979. E491D992. See p. 1383 (1 photocopied page) for a concise summary of the regiment's service.
Jenkins, David T., & James E. The Highest Praise of Gallantry: Memorials of…of the 146th New York Infantry & Oneida Cavalry. Farmville, VA: Farmville Printing, 2001. 72 p. E523.5.146th.M46.
New York (State). AGO. Annual Report...for the Year 1895. No. 7. Albany, NY: J.B. Lyon, 1896. pp. 193 219. E523.2N6no7. (Alphabetical roster of the regiment).
Phisterer, Frederick, comp. New York in the War of the Rebellion, 1861 1865. Vol. 2. Albany, NY:
Weed and Parsons, 1890. E523P584v2. See pp. 1187 88 (2 photocopied pages) for a brief history of the regiment and a roster of officers.
The following pertinent personal papers are in the Institute's Manuscript Archive:
Article on Company & James A. Cruthers History YeagerColl (Written in 1904 for Madison County Hist Soc)