All Erdogan can do is chest thumping against Assad, he didn't have the guts to go in for Turkmen, no one in Turkish government had it and ironically, Iran went in and helped to liberate Amerli.
Unlike you, Iraqi Turkmen are not obsessed with this whole blood master race nonsense and they surely saw what Turkey did for them: nothing. I was watching a report from BBC in a town around Amerli and their main commanders were all hailing Iran for sending weapons for them and organizing them and I'm sure I didn't hear the word Turkey from them even once.
Your ideas belong to to Third Reich era, this is 21st century. People tend to see who is there for them, not who shares blood with them.
You did nothing for Iraqi Turkmen, so expecting them to 'migrate' to Turkey is basically hallucinating.