Does Recurly Have a VAT MOSS Report?

No, Recurly does not offer a built-in VAT MOSS report. To obtain this data, you would need to use an export and create a report from that.

You can use the Invoices - Summary export, which is located under Analytics > Exports. This export includes a tax_amount and a tax_type column. You can filter by the tax_type column to only show the VAT tax collected and then use the tax_amount column to calculate the total.