Not only do you need a passport accepted by Spain, you also need a visa issued by Spain in Skopje.
A Schengen Visa issued by the the other members is not valid for Spain.
Unfortunately, the given link to their Embassy in Skopje does not work at the moment and the Foreign Office page gives no details. The EU page is a bit outdated (2016).
The Spanish consulate site in Hamburg (2018-10-29), states clearly that Kosovo passports are not reconized as valid travel document and that only one exception exists for the issuing of a visa.
Assume that you will be refused entry if controlled at the border.
If caught inside Spain without valid papers
- will face a heavy punishment
It would seem that Spain does not recognize Kosovo as a state, which would include their passports.
Travel to the EU from Kosovo - European External Action Service (2016-05-12)
Where can I travel to with a visa issued by Schengen States?
Short stay visas issued by the following Schengen States in Kosovo passports allow you to travel to all Schengen States except Spain, Slovakia and Greece:
Austria, Belgium, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Hungary, Iceland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Slovenia, Sweden and Switzerland.
The short stay visas issued by Spain, Slovakia and Greece are territorially limited to Spain, Slovakia and Greece respectively.
Embassy of Spain in Skopje:
Ul, 27 Mart, nº 7, 1000 Skopje, fYROM.
Tel: +389 2 3231 002/+389 2 3215 411
Fax: +389 2 3220 612
The Spanish Foreign Office Entry Requirements site gives no details of what of passport is required from Kosovo citizens.
Spezielle Einreisebestimmungen für kosovarische Staatsangehörige (2018-10-29, German only)
Special entry requirements for Kosovar nationals
As passports issued by the Kosovo authorities are not recognized by Spain, Kosovar nationals are not allowed to enter Spain with their Kosovar passport.
Exception: Family members of Union citizens.
Kosovo is not recognized by Spain as a state.
Therefore, Spain does not recognize Kosovan citizenship and also passports issued by the current Kosovar authorities, so they are not valid in Spain.
Kosovar nationals are not allowed to enter Spain with their Kosovar passport as they do not have a travel document recognized by Spain.