That is fairly easy, ohms law I = E/R where I is the current E is the voltage and R is the resistance. The tricky part can be figuring what the voltage is. For the base of the transistor that is 1 diode drop or .7 V, so the base resistor will have 4.3V across it (5V - 0.7V for the base diode.) to set the base current.
That is an easy place to start, although the output of the buck regulator should be keeping the supply voltage at 5V (there may have been a problem with the original resistor divider though.) I think the more likely problem is a low pwm frequency. This article
has some code (and an alternate, perhaps hardware based, pwm pin on pin5 instead of pin1) that may help. I wasn’t sure the attiny85 had hardware pwm, but it appears it does. You may be using software based pwm which will be slower and may be causing the flicker.