There is already an autonomous Kurdish region in Iraq that is functioning and actually more successful than Iraq itself. The US could help in establishing one in Syria however, as currently Rojava is a thriving anarchist-communist society.
The society in Syrian Kurdistan is functioning and based on the writing of Abdullah Ocalan has been more thriving than many of the surrounding states
The Kurdish people are a more forward thinking ethnic and religious group. They do not repress woman (in fact they hold woman as total equals to men), they do not oppress media, and are more liberal in their ideals. You do not see human rights violations within the Kurds like you do with other Middle Eastern nations, groups, and religions. A Kurdish nations would be
1. A huge ally of the US
2. Would help to bring democracy into the region
3. Would allow the Kurdish people a safe region to live
4. Would give oppressed peoples from Iran, Iraq, Syria, and even Afghanistan a safe place to relocate too
5. Would help spread human rights across the region
6. Would further destabilize terrorist organizations in the area
In addition the Kurds are putting up an amazing fight against ISIS and have enjoyed a lot of success. They are fighting and spilling blood to create an independent Kurdish nation. I believe through that act alone they have earned their independence.
Have we not learned what happened in Libya, Iraq, and Syria. Why is it we need to carve the world to our own liking and ignoring the religious and ethics diversity in that region . We as Americans have this dying urge, an unhealthy obsession to just go somewhere we don't know understand because we assume that democracy is a universally accepted form of government which is false. The Kurdish state won't be an ally because it'll be too unstable and easily subjected to enemies. And why should we care about the middle east being safe if we can't make Baltimore, St.Louis, Chicago, and Detroit better and safer. The reason why we have a massive immigrate problem in Europe and also why terrorism is so high today is because our involvement in the middle east for god sacks! These people don't want Americans stepping in the middle east anymore but we still do because we are appeasing the Saudi princes. I don't agree with the United States supporting helping create a Kurdish state because we have caused enough damage. In metaphorical terms the us is conducting a life saving surgery on a dead corpse.
The US should take a neutral stance on this. If the Kurdish people want their own country and a consensus builds between them and the countries they live in that this is the best path for the future then the US should support that. However, the US should not go out of its way to endorse an independent Kurdistan. This would alienate our allies, Turkey and Iraq in the region.
Realistically if there is ever an independent Kurdistan it will probably include land only from Iraq and Syria (and possibly Iran if there is a revolution in that country's future and the new government agrees to allow it). Turkey is strongly attached to that land and has a Turkish nationalist sentiment to back this up. Iraqis are less united, so a sort of "Velvet Divorce" could be possible. Turkey would oppose it because they would fear it would lead to rebellion in the part of historic Kurdistan that is in Turkey. There would at least have to be some kind of swearing off of that land by any new Kurdish government. Maybe Kurdistan could swear off that land but then allow any ethnic Kurd a "right of return", incentivizing Kurds living in that part of Turkey to leave and move to independent Kurdistan. Turkey might support such a deal since it could conceivably reduce ethnic tensions in that region.
If an independent Kurdistan is ever emerging the US should by all means help with diplomacy between conflicting interests to keep the peace, but the US should not take a stance for or against this sort of development.