It's a known fact that a wide variety of both generic and specially-engineered writing implements are currently used in space, by both the Russians and the US. But is there any known instance of a space traveller having used a fountain pen while in microgravity? If not, is there a specific reason why?
A fountain pen is unlikely to be used in microgravity as it is at least partially dependent on gravity to function.
The pen draws ink from the reservoir through a feed to the nib and deposits it on paper via a combination of gravity and capillary action. Source
It's hard to prove a negative. However, there is no documentation of usage by NASA.
A search for the phrase
"fountain pen" on the NASA Technical Reports Server returns 27 entries. Some of these documents are comparing something else to the size or shape of a fountain pen. Others are about using fountain pens for experiments or graphical arts on Earth. Three entries are about how law enforcement can detect the impressions on the lower sheets of a pad of paper left by pen writing on the torn-off top sheets. But there are no documents about using fountain pens in space.