MOSFET Gate Resistor Problem
The self-limitng current applies to a continuous current. Since you're driving a MOSFET, your concern is the peak current, and that's listed as 1.2 A. For a 14 V peak drive, the minimum resistor would be 14/1.2=11.67. But even here, the datasheet specifies 14 as the typical value, while the maximum is 16, so the new value should be minimum 16/1.2=13.33 -- choose a 15 Ω to be on the safe side.
But what you described with the two diodes and resistors is a way of having different edges for rising and falling time. For example the rising time might be needed to be slower, to reduce EMI, or give time to the other transistor in the leg to go off, while the falling edge will be faster, to drive out of saturation faster. Just an example assuming a half-bridge, looks like it's not the case.
Since you're not saying how you want to drive the transistor, all that a simple 15 Ω resistor will do is limit the maximum current, but in that same document you mentioned there are a few other ways to drive a MOSFET, out of which, given what I said above, you may consider the one at page 20, which is widely used. Or at page 18. It might pay off to use a driver, if only for the added protection for the IC: if the driver fails, you won't have to buy a new IC. But, again, without details, this is just a generic warning.