Funny enough, I went in search of a more discrete version of a graph/VU driver and came up with the same one Janitor Tzap posted above (go to the base URL of the picture and search for "VU meter LM324") in order to customize the resistor chain to deal with the non-linear sensor.
The quick way to get the values is to use a potentiometer with a base value of the full string (between the upper and lower isolation values, ie, the 2.2K chain), then apply the sensor voltage for your required trip points, and dialing the pot into the turn on voltage of the LM324. It'll be the same value to search for each time, but since you'll be increasing your input, you'll be increasing the bottom resistance of the pot voltage divider to get there. Measure the resistance between input side of the pot to the wiper each time and then you can build the network up from as close as possible to those values.
For the blinking, my thought is that you only want them to blink when needed, yet stay solid when not needed. Build your 555 timer for the frequency you want them to flash, then take a tap from one of the yellow LEDs (between the LM324 and current limiting resistor), invert and buffer it if necessary, and tie that to the 555 reset pin. That'll keep it turned off until the sensor falls low enough. Now for the flashing of the LEDs. For those that will be affected, change their main current limiting resistors to a much higher value, something that will let them work, but at a much reduced brightness. Now take a complentary number of small signal transistors and the correct value current limiting resistors and place them across the high value resistors, drive them from the 555, and you'll flash the LEDs bright/dim. You'll retain the graph ability since you are not actually supplying power, but an additional "signal" path.
Now Lenp has the easiest way to do it AND include features, if you know how to code. Just read the input, a bunch of IF/THEN/ELSE statements that include which ones to turn on and how they are treated (solid or flashing). Tempting. Unfortunately I am only versed in BASIC, so others will have to help there.
Here's another version to ponder: