As far as I know, « vingt douze » is never used in French.

The two ways you showed above are the only ways of saying years, except for the years of the last century. That exception is commonly used in Québec and in France. As an example, 1992 can be said:

• « mille neuf cent quatre-vingt-douze »,
• « dix-neuf cent quatre-vingt-douze »
• or « quatre-vingt-douze ».

Of course, you use the last one in a context, such as « en quatre-vingt-douze… ».

I have occasionally heard « dix-neuf cent … » , but « vingt cent … » would sound pretty weird. Neither of those has fewer syllables than the more standard « mille neuf cent … » or « deux mille … » .

Note that « mille » can also be spelled « mil » for years 1001 to 1999, though you can’t tell the difference in speech.