This answer is for the Netherlands, which was the original country in the question, before it was widened to Europe.
It is very hard to proof a negative, but I think you can not rent a Flevo Bike nor a Flevo Trike in the Netherlands at the moment.
In older comments I have found that the bike was not rented out but that you could rent the trike.
Net als met de FlevoBike kom je ook met de FlevoTrike in eerste instantie niet verder dan een meter of twee. Na een minuut of tien lukte het echter al redelijk om rechtuit te rijden; de Trike is beduidend gemakkelijker dan de Bike. De Trike wordt daarom wel verhuurd.
Like with the FlevoBike, with the FlevoTrike you do not get further than
about two meter on the first try. After ten minutes or so you will mostly manage to ride straight; the Trike is easier to ride than the Bike. The Trike is therefor available for rent. (Rough translation by me.)
From this website, in Dutch.
I have checked the sites of all recumbent rentals in the Netherlands as far as I could find them and non mention having Flevo Bikes or Trikes, nor for sale, neither for rent.
So my conclusion is that they are not for rent in the Netherlands at the moment.