Ammon and John as brothers is conjectural based on their children and death information for those children.
Sources
"Iowa, Armed Forces Grave Registrations, ca. 1835-1998," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:QL2K-M6QL : 11 February 2019), John Patrick, 15 Sep 1901; citing Norwalk, Warren, Iowa, United States, The State Historical Society of Iowa, Des Moines.; FHL microfilm 2,200,925.
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DNA Connections
It may be possible to confirm family relationships with John by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with John: