Is the word 'Netherlandish' correct English?

In certain contexts, yes. The OED defines "Netherlandish" as "of or pertaining to the Netherlands." Nothing could be simpler.

However, in the context of Art History, the work of the pioneering specialists in this area, Max Friedlaender and Erwin Panofsky, has referred to 15th and early 16th-century painting in regions now understood as part of the Netherlands, part of Belgium, part of France -- and well ....:

https://en.wikipedia.org/wiki/Early_Netherlandish_painting

Neth·er·lands (nr-lndz)

A country of northwest Europe on the North Sea.

Nether·landish (-lndsh) adj.

PROOF:
The American Heritage® Dictionary of the English Language, Fourth Edition copyright ©2000 by Houghton Mifflin Company.
Updated in 2003. Published by Houghton Mifflin Company. All rights reserved.

Shorter OED also mentions Netherlandian and Netherlandic.All synonyms of "Netherlandish" which according to OED can also be a noun referring to "the Germanic language of the Netherlands". By the way there was a time that locally the name "Nederduytsch" was used for the language. Which is not the same as Niederdeutsch or Plattdeutsch.

It is correct, but rarely used. Most people in the UK refer to the Netherlands as Holland in normal speech, and in any case tend to use the adjective Dutch referring to either Holland or the Netherlands.

Am I to conclude that "Netherlandish" is only (or mainly) used as a description of Dutch/Flemish art from the 15th and 16th century?

I would think so. I've never come across it, or Netherlandian or Netherlandic, both of which have a sound of being academic inventions.

Some linguists prefer the use of Netherlandic because that term is less confusing for them : language of the Netherlands in the original sense of the word, i.e. the Low Countries by the Sea. Dutch on the other hand simply means: language of the people, and originally also included German.
Written "Netherlandic" or "Netherlandish" evolved from the southern dialects spoken in the culturally advanced Flanders and Brabant of the 15th century. Spoken "N." grew out of the vernacular of the province of Holland, which became dominant after the 16th century. The existence of both a nationality-term Dutch and a linguistic term Dutch tend to create confusion. The terms Netherlandic/ Netherlandish is then seen as covering both 1. the speakers of "Flemish" variants of Dutch in the Flemish part of Belgium, which belonged to the ex- Southern Netherlands 2. the Dutch speakers in the present "Netherlands" ( the ex- Northern Netherlands)
Example: C.B. van Haeringen, a Dutch academic published a book on " Netherlandic Language Research", showing that he included the Flemish and Brabantian variants. See
http://columbia.thefreedictionary.com/Netherlandic+language
As to the history of the term Dutch see the OED.
Dutch = Hollandish, or in a wider sense Netherlandish, and even German. The OED's article on "Dutch" can be found at http://www.englishforums.com/English/Dutch/cbprw/Post.htm