In most states, legally if wipers are required for visibility, you must also have your headlights on. The issue isn't whether you can see or not, but whether others can see you. If you're in an accident in the rain and your insurance company finds out that you didn't have your lights on, they'll tear you a new one on the rate increase, even if you aren't ruled to be at fault from a police standpoint.
And the "flashers in heavy rain" bit is a little misleading. For rain to be heavy enough to warrant flashers, traffic would already be slowed to 5-10 mph. If you can still go 35+ mph, you don't need your flashers on.
ZV