Just got back from a few weeks away so have had a chance to find the FET I like to use. It is a 16N03L, data sheets here. The data sheet schematics should help you figure out how to connect up.
FET has a 30V 16A switch capability in a conveniently small leaded package (TO-251AA).
Not sure if they are still available as I acquired some old stock and the data stamp is 1996!
If you provide more details about what you are trying to achieve plus LED part number and desired flash frequency then that will help select a solution. Watch out for fault/error situations that may destroy your LEDs if they are not rated for 1.5A continuous, e.g. you make a mistake in your sketch and the logic output sticks high keeping the FET on! Add a resistor on the Arduino logic output pin to ground so the FET is kept switched off when the Arduino is being reset/booting/programmed.
Don't forget some high+low frequency decoupling (say 10nF + 100nF + 1000uF) on the LED supply voltage to absorb the inductive kick back that occurs when trying to switch off a high current quickly. Minimise lead lengths in the LED+FET+R+C loop.
A 15V supply (as suggested) is a better bet for reducing the current and hence inductive kick back from parasitic inductance in the wiring. Series LED forward voltage will be in the range 9V to 12V, hence the suggestion of a 15V supply. This means somewhere between 3V and 6V across the current limit resistors, hence a "select on test" value of 2.2 to 3.9 Ohms should be fine. I suggest a minimum 5W rated resistor (or 5 off 1W (10 to 22 Ohms) in parallel). Actual dissipation will depend on the ratio of on to off time.