The problem is that while the bicycle laws quoted above tell you that you need a light, they neither allow nor proscribe flashing lights. Rules on when flashing lights can be used are probably found elsewhere, probably the motor vehicle code. The Illinois Rules of the Road is a severe condensation of the code, it may discuss the use of four way flashers and it might mention other flashing lights. Or not. On the other hand quite a few of your fellow Illinois cyclists use rear flashers without any complaints from the police as far as I know. I have used a flashing front light as well all summer long, passing a couple of police cruisers a week without any complaints about that either. I think that either flashing lights are ok here, or else in the grand scheme of things they are not considered a big enough infraction on a bicycle to warrant enforcement.

I am pretty sure bicycles are not considered to be motor vehicles in Illinois, so the portion of the code quoted above is also ambiguous with respect to bicycles. If you can find language discussing horse drawn vehicles and flashing lights it may be broad enough to cover bicycles too.

Ken