Does anybody know how I reference FX rates in a Dashboard XFBR String rule?

you're unfortunately not going to have API's available to you in a BR string (only BRAPIs are available) so the above is not going to work. There are several ways to get at the FX rates, I will post two ways I've done it in a BR string before.
'Get rate type, time period, source And destination currencies
Dim objFxRatePkUsingNames As New FxRatePkUsingNames(""AverageRate"",""2018m1"",""EUR"",""USD"")

'Get the rate
Dim fxRate As Decimal = brapi.Finance.Data.GetCalculatedFxRate(si,currencyId.EUR,objFxRatePkUsingNames)

'Get WFTime Name
Dim timeName As String = BRApi.Finance.Members.GetMember(si, dimTypeId.Time, timeKey).Name
'Get FX Rate Type defined in RCM settings - this will be the rate type used to translate
Dim fxRateType As String = BRApi.Dashboards.Parameters.GetLiteralParameterValue(si,False,""StoredFXRateType_RCMT"")
'Get application currency defined in RCM settings - this will be the source currency
Dim sourceCurrency As String = BRApi.Dashboards.Parameters.GetLiteralParameterValue(si,False,""StoredFXAppCurrency_RCMT"")
Dim translatedUnexplainedLimit As Decimal = Nothing
'Get FX rates info
Dim objFxRatePkUsingNames As New FxRatePkUsingNames(fxRateType, timeName, sourceCurrency, destinationCurrency)
Dim objFxRateUsingNames As FxRateUsingNames = BRApi.Finance.Data.GetStoredFxRate(si, objFxRatePkUsingNames)

'for USD currencies, return the natural unexplained limit. For other currencies, translate the unexplained limit to local currency
If destinationCurrency.XFEqualsIgnoreCase(""USD"") Then

Return varUnexplainedLimit

Else

'confirm there is an FX rate, retrieve the rate and calculate the translated amt
If Not objFxRateUsingNames Is Nothing Then

Dim varFXRate As Decimal = objFxRateUsingNames.Amount