Or use a redirect command to "Chain" multiple API's, editing the source record to check the box first, then copying it.
Something Like this should work.....
// 1. Checks the box on the Source record being copied URLRoot() & "db/" & "_________" & "?a=API_EditRecord&rid=" & URLEncode ([Record ID#])
& "&_fid_30=true&apptoken=_____________________
&rdr=" // 2. The RDR above cycles to a second API Call type to copy that same source record...URLRoot()&"db/"________?a=GenCopyRecord&rid="&[Record ID#]
You could also solve for this with actions or automations, which are a bit more user friendly. Depending on the use-case, checking the box on the source record and saving could be used as an "Automation" trigger that copies the values from that record to another, but the API route is a bit more elegant IMO.