What happens when we write delay instruction twice continuously in an MSP430

My suggestion would be get rid of the delay function and use the built in if you are using IAR or CCS."__delay_cycles (cycles);" using the built ins, will give you more predicable results and better timing. You could probably just replace your delay for the built in, to get closer to the results you are looking for.

personally I would go about the whole thing using interrupts and timers to pull the whole thing off and use the peripherals that the msp430 has. I would suggest using the WDT as an interval timer, doing this would leave the other timer for your motor control. p1.3 is used as the wake up pin and p1.0 is the led pin.

example code

volatile int counter;
void main(void) {
    WDTCTL = WDTPW + WDTHOLD;                 // Stop watchdog timer
    P1DIR = 0x01;                             // P1.0 output, else input
    P1OUT =  BIT3;                            // P1.3 set, else reset
    P1REN |= BIT3;                            // P1.3 pullup
    P1IE |= BIT3;                             // P1.3 interrupt enabled
    P1IES |= BIT3;                            // P1.3 Hi/lo edge
    P1IFG &= ~BIT3;                           // P1.3 IFG cleared
    _BIS_SR(GIE);
}
// Port 1 interrupt service routine
#pragma vector=PORT1_VECTOR
__interrupt void Port_1(void)
{
    WDTCTL = WDT_MDLY_64; //enables intervals of 64mS
    IE1 |= WDTIE;  // set WDT interrupt
}
#pragma vector=WDT_VECTOR
__interrupt void watchdog_timer (void)
{
    ++counter;
    P1OUT |= BIT0;
    if (counter == 245) {  //245 x 64mS = 15.6 seconds
        P1OUT &= ~BIT0;
        WDTCTL = WDTPW + WDTHOLD; 
    }
}

Not complete nor has this code been tested, but it should turn the led on for 15 seconds every time the P1.3 button is pushed.

The Family Reference Manual has timing info for various instruction starting on page 63. The number of cycles is not fixed for a certain instruction, it appears to be dependent on the mode used. Here is one of the tables from the manual, you can see most instructions take more than 1 cycle:

I haven't used an MSP4340, but I imagine there should be a tool available in the IDE to time your code and tell you how many cycles it takes to run. I'd try and find/use this first - if you can't, use the info in the manual and calculate manually.

If you tell us more about the device that needs the data (part number, format, etc) then we may be able to suggest alternatives (e.g SPI peripheral?). It sounds like a tall order to achieve this speed using this method, and not particularly efficient if a peripheral/PLD can do it for you.
With the price/capability of uCs nowadays, needing to resort to stuff like this is usually a sign for me that I need to consider moving to a more capable uC (unless the quantities are such that it makes enough of a difference)