If I have a pending DUI warrant, can I fly out of the county and be allowed to return?

Unless your conditions of release required you to stay in state, you generally can leave the state pending the resolution of your case, so long as you appear for your court dates.  If you've missed a court date and have not resolved that problem, you should make sure you resolve it before you leave the state.

While it's unlikely that the police would even know you left the state, if they do find out you left the state and are interested in pursuing you, they could accuse you of fleeing the jurisdiction if you haven't gotten your missed court date taken care of.

Unless you're an illegal alien, I doubt that this would be an issue.  It's possible, though, that you might be arrested on your return.  What I'd suggest is contacting the court, and arranging to post bail;  when you do that, you can also see about scheduling your court date for after your return.  That way, the warrant will be recalled.  Until you do go to trial, you haven't been convicted of anything, and it wouldn't be a reason to prevent you from returning.

If you do have any immigration issues, you need to talk to an attorney who practices in that field of law, because the cases tend to be very fact-specific.

Generally, airlines are not tied in to the criminal system so when you purchase your ticket you will not be arrested.  Same holds true when you return on your flight.  The only time that you would be restricted on your flight is if you are on the "do not fly" list, which I am assuming that you are not.

You really do need to take care of the DUI and the pending warrant as soon as you can.  You do not need to live in fear that you may be arrested.  It is good that you have not been driving in the meantime.  And yes, it will probably cost you a good amount of money for a good lawyer but it will be worth it in the long run. Good luck with everything.