Your dad is correct about the LEDs not drawing enough current. As far as the resistor value not mattering, well, I know that resistors control the amount of current going through something, and the brightness of LEDs is determined by how much current is allowed to pass through each LED.
Usually, if you buy them from places such as www.superbrightleds.com or www.ledtronics.com, they make bulbs with several LEDs with resistors inside the bases. Unless they are wiring them up in parallel, I don't see this necessary if wiring up more than 5 LEDs(@3volts each) because the LEDs will spread the voltage across the series.
Anyway, I'll stop rambling....

There are a couple things you can do to fix this.
1) if you have a thermal flasher, you need to replace it with an electronic flasher. Just turn your car on, put the blinker on and listen to where its coming from, should be under the steering wheel, above the pedals in all the wiring mess. An electronic blinker looks like a smal soda can. Its cylindrical.
When and if you have an electronic flasher, wire up what is called a "dummy load," to the blinker wiring. What these do is "trick" the flasher into thinking that the LED bulb is pulling enough current. They go for about $4 each.
2)Buy an LED electronic flasher. They run about $50 and you just replace your stock one with it. You don't have to wire dummy loads or anything, just plug and play and your LED blinker bulbs should work.
Here's a website where you can get those 2 things
http://www.watsons-streetworks.com/leds_plus.html
Hope that helps,
Ed