Here are some books and papers about asian playing cards :

General

Korean Games with Notes on the corresponding Games of China and Japan

Writen by Stewart Culin (1858-1929), published in 1895, (see his bio here).
This book describes the card games played in China in the late 1800's, based on the collection of MR W.H. Wilkinson, owned by the Museum of the University of Pennsylvania (Pages 135 to 147).
Archive.org

Ostasiatische Spielkarten (East Asian Playing Cards)

Written by Gernot Prunner (1935-2002), (see his bio here).
Published by the Hamburgisches Museum Fur Volkerkunde Und Vorgeschichte in 1969.
This book describes the east-asian cards found in this museum, written in German.
This book is available at various second-hand books websites.

The card games of asia and their cards アジアのカードとカードゲーム : 中国はカードゲームの故郷か

Written by 梅林勲 published in 2000
A very rich description of card games of Asia, in Japanese.
This book is available on international bookshops websites.

Vietnam

Books by Trần Gia Anh

This Vietnamese author from Hanoi has written a lot of books about games, here are 3 books about playing cards in Vietnam (in Vietnamese) :
Phong tục tập quán Việt Nam đặc sản Bài Lá (2010)
Bài lá ở Việt Nam Luật chơi (2011)
Bài lá ở Việt Nam Luật chơi (2003)
These books are available on Vietnamese websites.

Bí quyết bói bài tứ sắc

Written by Pierre Do Dinh
This book is about playing Tu Sac, written in Vietnamese.

Le To-Tom Jeu de Cartes Annamites

This paper, in French, written by Nguyễn Văn Vĩnh (1882-1936) (website), explains in details the rules of To Tom.
It was first published in Annam Nouveau in 1932 and reproduced in Bulletin de la Société des Etudes Indochinoises Tome XXVIII, N.4, 4e trimestre 1953.

Connaissance du Vietnam

Written by Pierre Huard and Maurice Durand in 1954 (French language).
This book is about Vietnamese Culture, pages 243 to 246 are about playing cards.

Le Tam Cúc et le Bát

Written by René de Creissel, published in Revue Indochinoise, jeudi 30 novembre 1944, n.222.
This paper, in French, explains how to play the games of Tam Cúc and Bát.
(Thanks to Alain : website, here is his index of Revue Indochinoise and his retranscription of this paper)

Chinese books

中国纸牌的玩法

Written by 胡柏生 published in 2000
How to play the Nan Tong cards.

南通长牌 话说搭子和

Written by 胡柏生 杜国元 published in 2010
This is a new edition of the book above.

Chinese Language papers

The Playing-Card

This journal edited by the International Playing-Card Society (website) has published some papers relating to Chinese Playing Cards :

Java and Malaya

The manners and customs of the Chinese of the Straits Settlements

Written by Jonas Daniel Vaughan (1825-1891), published in 1879 (see his bio there).
This book contains a whole chapter about the playing cards used by the Chinese in the Straits Settlements (Singapore/Malaya) and includes drawings of the cards (Pages 65 to 82).
Cornell University

Javaanse Kaartspelen

Written by Dr. Tjan Tjoe Siem, published in 1941.
This book, written in Dutch, contains a full description, with images, of the Ceki packs with the names of the cards in the various parts of Indonesia.

Gambling games of Malaya

Written by C.T. Dobree published in 1955
This book describes the gambling games played in Malaya in the first half of the 1900's.
This book is quite rare. Some libraries can make digital copy of some pages.
There are books in Indonesian and Malaysian languages too, here are papers in English and Dutch.