Cani, as it is, sounds to me as a diminutive of
canijo, but is also a urban tribe (refers to people from the suburbs, violent and without much education. Is more or less what some people address by "white trash").
Cañí, with the 'ñ' is indeed an adjetive, that means both "gypsy" and "typical or folklorical"
La España cañí is a set phrase that refers to folkloric Spain and is sometimes used derogatorily. It must be distinguished from cani, a violent urban tribe of Spain.
cañí can used refer to gypsies, but I have never heard it to actually call somebody "gypsy" if they are not (Also, probably we favor
gitano to designate the race, although could be be referred as
calé as well. They call the non-gypsy people