There is currently no centralised international database but the object specific database BeSS for professional and amateur spectra of Be stars makes an excellent model for such a general database.
This is a professionally funded high quality system with moderation of submitted data and a mentoring service for amateur contributors run by pros and amateurs. There were thoughts to expand it but it would need funding. I have been talking with AAVSO for many years about this (including advising several of the various working parties there have been over the years) and the people behind BeSS have offered the complete system to AAVSO to use but they appear to want to go their own way against the advice of other experienced amateurs in this area and I have currently given up on them.
In the meantime the most complete source of amateur spectroscopic data is the ARAS organisation who have been archiving spectra submitted to them on a range of objects
(although unofficial, ARAS is where most serious amateur spectroscopists can be found and they are currently the main force driving up standards in this area)
I plan to talk more about how ARAS is functioning at the upcoming VSS meeting using Nova Del 2013 as an example