Chip Resistor Power
It is clear that the AVERAGE power dissipation in your application is well within the rating of your chip resistor, so the question is only whether the resistor will be reliable with the power-time product of the individual pulses in your pulse train.
My intuition, like the other posters, is that you are very safe, but the proper evaluation would consider the thermal time constant of the mounted resistor. That is, for a step change in current, the time it takes for the resistor to reach 63% of its final temperature is the thermal time constant of the resistor as it is mounted on the board. If that time constant is much longer than the duration of the individual current pulses in your application, then the average power dissipation is the determining parameter. If the thermal time constant is comparable to or shorter than the duration of pulses in your application, you are in trouble because the resistor will respond thermally to the peak power of each pulse.
You can use a very fine thermocouple epoxied to the resistor chip to measure the time constant. You don't even need a precision readout or cold junction reference, since you don't really need the true temperature, just the change of temperature. In fact, you don't even have to determine the true time constant. Just look at the amplified TC output on a 'scope as you apply the worst-case pulse train in your application. You need enough amplification to see a small change in temperature when you start your pulse train, showing that you are actually seeing the thermal response of the chip. If you do not see any significant response to the individual pulses, the thermal time constant is long compared to your pulse durations and you only have to be concerned about the average power dissipation. If you see the temperature ramping up and down in synchronism with your pulse train, it is responding to each pulse and either more detailed thermal analysis or more conservative design is required.
I doubt that it is worth your time to perform this measurement, but it is really easy to do and would give you confidence in your design. See OMEGA for thermocouples. The bead and the wires must be very small compared to the chip so they do not add significant heat sinking to the chip or conduct significant heat away from the chip. Use a pair of TCs in series bucking configuration with one attached to the chassis or a handy thermal mass and the other attached to the chip. This will cancel out the ambient temperature and show the differential temperature between the two beads. You don't care about the calibration for this test.
Have fun.
awright