Whenever I turn my headlights on my turn signals dont flash anymore they just stay solid. Turn signals flash normally without headlights on.

 

Your car should do the same thing with just the parking lights on.

9 times out of 10........

You have a bad or non existent ground connection on one or more of your turn signal light bulbs.

It can be a corroded bulb socket or wire connection to sheet metal, broken wire, or internally shorted bulb.

When there is no ground for your turn signals, the bulb will "back feed" it's ground connection thru the remaining good parking circuit and blink as normal.

When you turn on the parking lights, that back-fed ground is eliminated, and the turn signal will no longer flash.

Check grounds, sockets, and bulbs.

 

I had this same exact issue and it was a bad ground on my rear lights. Instead of following the ground from the back all the way to the front, I just added a ground near the backlights.