I found some game write-ups and box scores for the games here. The first link top left has one. New York Historic Newspapers is a great site and recommend it for research. If you find anything interesting about the team, please post it. The name Keleher is interesting. There was a middling player for the Brooklyn Robins of the same name, who was out of professional baseball at the same time that the Kingsbridge Athletics were playing. Maybe they were the same guy? Probably not but I would be interested to know for sure.
If you are looking for more information than that, there could be something in the Riverdale News newspaper. The Lehman College library has issues dating from 1915. Next time I am there I will have a look at that time period and get back to you.
Can you post a picture of the Dyckman Oval?