I made this game about 40 years ago when a deck of cards was much easier to carry around and play games with. Over the that time it's had a few minor iterations, but is largely the same game where it plays a lot like chess with the exceptions of only covering opponent pieces rather than taking them off the board, and being able to move through your own coloured pieces. 

Here's the current ruleset (  originally posting in 2007 at Down to the Bones ...: Card Chess (vrbones.com) )

CARD CHESS GAME CONCEPT

- A game for 2 players with a standard pack of cards inspired by chess.
- One player is 'red', the other 'black'
- Each player has an army of 2 Kings, 2 Queens, 2 Jacks and 2 tens of the colour they are playing.
- Players take turns to move one of their units in any allowable direction, as in chess.
- Instead of 'capturing' pieces, an attacking move is to simply 'cover' your card over an opponents. A covered card cannot move. If the card on top moves off to another position, the uncovered card is now back in play and can move freely once again.
- Since there are 2 kings, the game ends when one side has covered both kings.

THE PLAY SURFACE

- The remaining 36 cards are aligned in a 6x6 grid to form the playing surface. It is broken up into 3 6x2 areas; Black's starting area, the terrain, and Red's starting area.

BBBBBB
BBBBBB
TTTTTT
TTTTTT
RRRRRR
RRRRRR

B = Black starting area
T = Terrain
R = Red starting area

- Cards making the startup areas of the playing surface are played face down.
- To create the middle Terrain, shuffle all 2,3 & 5 cards (12 cards in total) and deal into place. This should give 6 red terrain segments and 6 black terrain segments.

MOVING AND ATTACKING

- A King's movement is similar to a King in chess (one space in any direction). A queen moves like a queen in chess (horizontally, vertically or diagonally). A Jack moves like a bishop (diagonally). A Ten moves like a castle (horizontally & vertically).

- When moving in a direction (horizonally, vertically or diagonally), your unit may stop at any card on the playing surface in that dirction up to and including the first card of the opposing colour. EG: Playing Red would mean that Black terrain cards and black unit cards stop further movement. As a reverse of this, you can pass over or land on any turned over card on the playing surface, any terrain of your colour, or any card of your army.

SETUP

2 modes of setup are currently used; one for beginners and quicker play, and one for a more competitive, balanced start.

1. Fixed starting positions

- Each player sets out their army in the same format as below:

TQKKQT <--- Black army
.   .  J J   .   .
.  .   .   .   .   . 
.  .   .   .   .   . 
.   .  J J   .   .
TQKKQT <--- Red army

T = Ten
J = Jack
Q = Queen
K = King

- You may wish to have cards of the same suit together (EG Diamons on left, Hearts on Right), but as there is no distinction between suits in the game, it is not important)
- This method give the players a known starting position with a random terrain in the middle to give slight variablity (you can even play without the terrain in the middle for training purposes with people that may not be familiar with chess movement)
- As with chess, the player starting first has a slight advantage.

2. Progressive starts

- Each player starts with all unit cards in hand and the playing surface completed.
- Decide who will play first, via coin toss or mutual consent
- Players take turn placing any unit in hand anywhere in their starting area that has not already been occupied. Players should keep in mind the terrain in play and also currently placed cards to judge the most effective position for the placed card.
- When all cards are placed, the starting player can now move units.
- The starting player's advantage of moving first is balanced by their opponent who places the last card in the setup phase