referencing a column value in R part of a R1C1 formula

If I understand the request then you should be using a SUMIFS() function

e.g. ij J164.

Formula:

=SUMIFS(J136:J155,H136:H155,2019)*0.085*J2

And is there a typo since you haven't included J149?

You can also create dynamic named ranges:
Data_Periods ='103'!$J$4:INDEX('103'!$U:$U,COUNT('103'!$D:$D)+3)
DataYear ='103'!$H$4:INDEX('103'!$H:$H,COUNT('103'!$D:$D)+3)
MajorAccountID ='103'!$D$4:INDEX('103'!$D:$D,COUNT('103'!$D:$D)+3)
pro_rated_inflation ='103'!$J$2:$U$2

Then:

   ActiveCell.FormulaR1C1 = _
        "=SUMIFS(INDEX(Data_Periods,0,COLUMN(R1C[-9])),MajorAccountID,6000,DataYear,RC8)*0.085*INDEX(pro_rated_inflation, COLUMN(R1C[-9]))"

Or, instead of writing a formula to the cells, calculate and write the sums with the macro:

Option Explicit
Sub TaxExpense()
    Dim Acct6000    As Range, _
        AcctDescr   As Range, _
        AcctRec     As Range, _
        ProRateInfl As Range, _
        Counter     As Long, _
        TaxExpRow   As Long, _
        VarianceRow As Long, _
        Accumulator As Double, _
        t0          As Double, _
        TaxYear     As Variant

    t0 = Timer
    With Application
        .ScreenUpdating = False ' turn off screen flicker
        .EnableEvents = False ' turn off events
        .DisplayAlerts = False
        .Calculation = xlCalculationManual
        .AskToUpdateLinks = False 'suppress asking for update
    End With
            
    With Range("D:D")
        Set Acct6000 = .Find(6000)
        Counter = WorksheetFunction.CountIf(Range("D:D"), 6000)
        Set Acct6000 = Acct6000.Resize(rowsize:=Counter)
    End With
    
    For Each TaxYear In Array(2018, 2019)
        'find the row to insert PERIOD SUMS
        For Each AcctDescr In Range("G:G")
            If AcctDescr.Value = "PAYROLL TAX EXPENSE" And AcctDescr.Offset(ColumnOffset:=1).Value = TaxYear Then
                TaxExpRow = AcctDescr.Row
            End If
        
        'find the row to insert variances
            If AcctDescr.Value = "PAYROLL TAX EXPENSE" And AcctDescr.Offset(ColumnOffset:=1).Value = "Variance" Then
                VarianceRow = AcctDescr.Row
                Exit For
            End If
        Next AcctDescr
            
        'Total up expenses for each period
        For Each ProRateInfl In Range("J2:U2")
            For Each AcctRec In Acct6000
                If AcctRec.Offset(ColumnOffset:=4).Value = TaxYear Then
                    Accumulator = Accumulator + AcctRec.Offset(ColumnOffset:=ProRateInfl.Column - AcctRec.Column).Value
                End If
            Next AcctRec
            
            'format total
            Accumulator = Round(Accumulator * 0.085 * ProRateInfl.Value, 2)
            
            ' ** write to tax expense cells **
            
            Cells(TaxExpRow, ProRateInfl.Column).Value = Accumulator
        Next ProRateInfl
    Next TaxYear
        
    With Application
        .ScreenUpdating = True
        .EnableEvents = True
        .DisplayAlerts = True
        .Calculation = xlCalculationAutomatic
        .AskToUpdateLinks = False
    End With
    MsgBox Round((Timer - t0), 3) & " Sec"
End Sub