Is there a way to get Step Functions input values into EMR step Args

Parameters allow you to define key-value pairs, so as the value for the "Args" key is an array, you won't be able to dynamically reference a specific element in the array, you would need to reference the whole array instead. For example "Args.$": "$.Input.ArgsArray".

So for your use-case the best way to achieve this would be to add a pre-processing state, before calling this state. In the pre-processing state you can either call a Lambda function and format your input/output through code or for something as simple as adding a dynamic value to an array you can use a Pass State to reformat the data and then inside your task State Parameters you can use JSONPath to get the array which you defined in in the pre-processor. Here's an example:

{
"Comment": "A Hello World example of the Amazon States Language using Pass states",
"StartAt": "HardCodedInputs",
"States": {
    "HardCodedInputs": {
        "Type": "Pass",
        "Parameters": {
            "cluster": {
                "ClusterId": "ValueForClusterIdVariable"
            },
            "time": "ValueForTimeVariable",
            "daysToLookBack": "ValueFordaysToLookBackVariable"
        },
        "Next": "Pre-Process"
    },
    "Pre-Process": {
        "Type": "Pass",
        "Parameters": {
            "FormattedInputsForEmr": {
                "ClusterId.$": "$.cluster.ClusterId",
                "Args": [
                    {
                        "Arg1": "spark-submit"
                    },
                    {
                        "Arg2": "--class"
                    },
                    {
                        "Arg3": "com.some.package.Class"
                    },
                    {
                        "Arg4": "JarUri"
                    },
                    {
                        "Arg5": "--startDate"
                    },
                    {
                        "Arg6.$": "$.time"
                    },
                    {
                        "Arg7": "--daysToLookBack"
                    },
                    {
                        "Arg8.$": "$.daysToLookBack"
                    }
                ]
            }
        },
        "Next": "Some Step"
    },
    "Some Step": {
        "Type": "Pass",
        "Parameters": {
            "ClusterId.$": "$.FormattedInputsForEmr.ClusterId",
            "Step": {
                "Name": "FirstStep",
                "ActionOnFailure": "CONTINUE",
                "HadoopJarStep": {
                    "Jar": "command-runner.jar",
                    "Args.$": "$.FormattedInputsForEmr.Args[*][*]"
                }
            }
        },
        "End": true
    }
  }
}

You can use the States.Array() intrinsic function. Your Parameters becomes:

  "Parameters": {
    "ClusterId.$": "$.cluster.ClusterId",
    "Step": {
      "Name": "FirstStep",
      "ActionOnFailure": "CONTINUE",
      "HadoopJarStep": {
        "Jar": "command-runner.jar",
        "Args.$": "States.Array('spark-submit', '--class', 'com.some.package.Class', 'JarUri', '--startDate', $.time, '--daysToLookBack', '$.daysToLookBack')"
      }
    }
  }

Intrinsic functions are documented here but I don't think it explains the usage very well. The code snippets provided in the Step Functions console are more useful.

Note that you can also do string formatting on the args using States.Format(). For example, you could construct a path using an input variable as the final path segment:

"Args.$": "States.Array('mycommand', '--path', States.Format('my/base/path/{}', $.someInputVariable))"