I would say I pronounce 'platinum' with three syllables, however the second syllable is so short it might be indistinguishable in connected speech. I say 'platinum' as [ˈplɑ:ʔənm] (that is a syllabic 'm', but I can't find the diacritic).
Dictionaries will likely show it as two syllables. Dictionary.com says /ˈplætnəm/. Interestingly my own Oxford dictionary has /ˈplætməm/. I'm not sure if this is a typo