Constant current Opamp circuit issues
It's a wonder you get 1.5A at all.  

edit
Since you mention 3.3V as the input for your boost regulator I'll presume that this is also the power supply for your 555 and opamp. The LM555 doesn't work at this low voltage, so you'll have to use the CMOS version, TLC555.   

\$H_{FE}\$ for the 2N5191 at 1.5A is minimum 25, so you'll need 60mA of base current. An \$H_{FE}\$ of 25 makes that the opamp sees the 0.5\$\Omega\$ emitter resistor as 12.5\$\Omega\$. That's still low, so it won't be the limiting factor for the base current: \$\dfrac{3.3V - 0.7V}{12.5\Omega}\$ = 208mA.  

The problem is the opamp. At 2.5V power supply the MCP6021's short circuit current is typically 30mA, which in a worst case situation will only give you 750mA collector current. The reason you do get 1.5A is that the 25 is the transistor's minimum \$H_{FE}\$, it can go up to 100.  

The \$H_{FE}\$ you get is typical for a power transistor, so swapping it for another type probably won't help much. You can use a Darlington, or make your own by adding a small signal transistor to drive the power transistor's base. The BC817 will be suitable.  

A MOSFET is also a possibility, but this should be chosen with care. Even logic MOSFETs don't always give their maximum current at 5V \$V_{GS}\$, and the sense resistor subtracts also a certain voltage from it. The 555's output divider gives 1.65V for the opamp's non-inverting input, and given enough drive current the sense resistor will also settle to 1.65V, giving 3.3A to the LEDs. That means that the MOSFET should be able to give 3.3A of drain current at only 3.3V - 1.65V = 1.65V \$V_{GS}\$. That's very low! But by a lucky coincidence an answer to another recent question showed this graph:  

  

That damned AO6408 delivers 8A at only 1.5V \$V_{GS}\$! Tailor-made for the job!