Perhaps Kerry didn't notice, but just a few days before his threats, the OAS took a resolution that Washington brought against Venezuela and turned it inside out, declaring the regional body's "solidarity" with the Maduro government. Twenty-nine countries approved it, with only the right-wing governments of Panama and Canada siding with the U.S. against it.
Article 21 of the OAS' Democratic Charter applies to the "unconstitutional interruption of the democratic order of a member state" (e.g. like the 2009 military coup in Honduras that Washington helped to legitimize, or the 2002 military coup in Venezuela, aided even more by the U.S. government). Given its recent vote, the OAS would be more likely to invoke the Democratic Charter against the U.S. government for its drone killings of U.S. citizens without trial, than it would be to do so against Venezuela.