I have a side by side KitchenAid refrigerator with ice and water in the door. Recently, the water dispenser pressure started to decrease noticeably, but the fridge still made some ice. When I put in a new filter, there was a great gush of good pressure water dispensed for about 10 seconds, and then it went back to a trickle. Now the ice has stopped making , and the water dispenses in drips.

I've read that I need to try and flush the line, but I'm not sure how to do that. Any advice?

Can you bypass the filter? If it doesn't have a bypas try connecting water line atound it temp. This will give you more pressure to clear lines Then after you believe lines are clear, reconnect filter. The filter does reduce pressure a little. I have blew through the lines before at the line hust past filter with low pressre air such as one of those small electric air air pumps