1/4 inverted flare to AN fitting? Does it exist? Trans cooling line issues

That is most certainly a female inverted flare, not 1/4 NPT. I can't tell what the size is from just a picture but it's probably a 5/16 or 1/2 inverted flare fitting. Here's a link to all of Summits inverted flare to AN adapters. Summit's customer service is stellar. If you give them a call, they may well send you the adapters you need for free. Tell them exactly what part number you ordered, the description on their website and tell them you can send them a pic. Make sure you call tech support, not sales. I hope you didn't try to crank the 1/4 NPT fitting in as that will ruin the threads. Here's a pic of what you need to make this work:

Edit: I'd also try to get rid of that gunk in the one picture at the bottom of the hole. That could cause a leak.

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