I have a warant for "failure to appear on suspended license. Can I fly to another state{S.C.} without being arrested at the airport in detroit ?

If you do you would be adding to your charges.
Are you wanting to go to S.C. to run or did you have something you had planned like a visiting family?
If you are trying to run you would never be able to get a drivers license in any state.
If it was a planned thing you need to talk to somebody and get it all taken care of then maybe you will have time to go to S.C. after.

If you are asked to produce identification at the airport what are you intending to use - your suspended driver's license? I would not fly anywhere using that as id. They may decide to detain you at the airport if you produce any kind of id that is expired or suspended once they run it through their terminal. Are you willing to risk this? You need to clear this up before you go anywhere as you could end up in jail for a lot longer than you wish.

Can you, maybe, can it show up on the background search for your name, yes, Can the police be there at the gate to get you when you come back, my guess is yes, but maybe not.

Best bet, take care of the warrant, set up bail and be free to travel