It helps considerably when you post where the person lived, died, who he married, etc.
Based on what others posted on Rootsweb I found enough to find the right Charles H. Brink in several census records:
1900 Walnut Grove Twp., Greene Co., MO: Charles H. Brink, born July 1832 in Pennsylvania. The 1880 census shows much the same info. The 1890 veteran census shows he was in Company H, 1st Cal. Calvary Regiment 1864-1866. It's hard to find him before that with any certainty.
His Civil War pension numbers are Appl 256544 Cert 427510 Widow Appl 816535. You can request a copy from the National Archives in Washington, DC for $75. While Civil War pension vary in what genealogical data they contain his pension may have the very info you are looking for. As I understand it the pensions will eventually be online but I don't know the timeline. Some are already online at Footnote.com for a fee.
His obituary just might list his siblings. I see he was buried in the Springfield National Cemetery.
Unfortunately his Missouri death certificate doesn't help to find his parents. His obit might list siblings.
Census records have him in Buchanan County, MO in 1910, 1900 and 1880. The 1870 census has him in Troy, KS. All of them have him born in Indiana. Where his parents were born varies but most likely his mother was born in KY. It's hard to find him before that with any certainty.
James also had a Civil War pension Appl 1381798. Served in 10th U.S. Cavalry. He applied March 13, 1909. It doesn't look like it was approved, but the application would still have info he supplied to get the pension.
Some of these records you can look at for free at labs.familysearch.org and Ancestry.com. For those you cannot see for free I suggest checking with your local libraries to see if they have Ancestry or Heritage Quest.