That circuit may work as drawn with some combinations of LEDs and battery voltages, but it's bad practice to drive LEDs without current limiting resistors. When your battery voltage starts to drop, the LEDs will become a lot dimmer quite quickly.
The best way to drive high power LEDs is using MOSFETs but they don't tend to work well at 3.6V unless you get specialised modern ones that are only available in SMT (surface mount). For your case I suggest using two PNP transistors driven from the collectors of the NPNs and acting as buffers, with current limiting resistors, like this.
View attachment 14848
I've increased the base resistors from 4k7 to 47k and reduced the capacitors accordingly, just to save power. You don't need to make that change if you don't want to.
Q3 and Q4 are driven from the outputs of the astable multivibrator (oscillator) circuit and they provide buffered drive to the LEDs. You can calculate the LED current limiting resistors using the guidelines and formulas in Steve's tutorial at
https://www.electronicspoint.com/resources/got-a-question-about-driving-leds.5/
Q3 and Q4 will drop about 0.2~0.3V so you need to take that into account.
You may need a higher battery voltage to get a reasonable voltage drop across the current limiting resistors for stable LED brightness.