Yes, Floorify vinyl floors are installed floating and so can be installed on any stable and sturdy surface. As such, you can lay a Floorify floor on top of your glued or nailed parquet.
Some examples for an underlay in wood:
Ensure that the subfloor is level and nail any loose parts down. Check the floor for signs of mould and/or insect infestations. Use a levelling board or levelling compound to prepare the subfloor, if necessary. Make sure that the crawl space between the floor and the wooden subfloor is well ventilated at all times. Remove any obstacles and ensure that there is sufficient ventilation (minimum of 4 cm² total ventilation openings per m² floor). Always check the moisture content of the wooden subfloor. This must never exceed 10%.