Hi and welcome.
Bad news. High current leds like those can't be used in the same way as "normal"/5mm leds. Transistors won't really help.
The two problems are (1) current limiting and (2) heat dissipation.
With ordinary 5mm leds, you have a series resistor designed to drop some of the supply voltage or output pin voltage down to what the led needs. Because the current involved is small, e.g. 20mA, this is no problem for the Arduino pin to supply, and does not generate any noticeable heat in the led. The series resistor will also be dissipating some heat, but again this will not be noticeable at these low currents, so 1/4 Watt resistors are normally fine.
With these high current leds, the heat problems become much more serious. The led itself must the soldered to a large heatsink, or it will very quickly die.
The second problem is the series resistor that would be needed for such a large current. A series resistor would need to drop 2.9V (assuming a 5V supply), so the resistor value would need to be around 5 Ohms for 700mA current. The resistor would need to dissipate around 2.5 Watts.
In theory, you might be able to find such resistors, but they would be large & expensive and still get quite hot. Your power supply would also need to be large and provide a lot of current, most of which would simply be wasted as heat by the series resistors.
Unsurprisingly then, series resistors are not used with high current leds. Instead, a circuit known as a "Constant Current Source" is used, which adjusts its output voltage to ensure just the right amount of current flows through the led, without needing a series resistor and wasting masses of power.
So you need 3 of these constant-current led drivers, one for each led, and you need a design that has a PWM input that you can connect to the Arduino pins to allow you to fade each colour.
Hope this helps.
Paul