A feature not completely illustrated by the block diagram is the LED brightness control. The current drawn out of
the reference voltage pin (pin 7) determines LED current. Approximately 10 times this current will be drawn
through each lighted LED, and this current will be relatively constant despite supply voltage and temperature
changes. Current drawn by the internal 10-resistor divider, as well as by the external current and voltage-setting
divider should be included in calculating LED drive current. The ability to modulate LED brightness with time, or
in proportion to input voltage and other signals can lead to a number of novel displays or ways of indicating input
overvoltages, alarms, etc. Source: LM3914 datasheet page 9.
As Dave Tweed points out and the datasheet clarifies, the minimum current is determined by the internal reference network.
If you really need to dim it you could consider a PWM feed on the LED anodes (positive supply to all the LEDs).
Figure 1. PWM signal transitioning from high pulse width (75%) to low (25%) and back again. Note amplitude remains constant. If used, this will result in brightness control respectively giving 75% and 25% of full brightness. Image source: mine.
A web search for a 555 PWM control circuit with switching frequency set at > 100 Hz should appear flicker free.