no he would not be held liable...
yes, he was the breaching party and under contract law would be held to damages which include only restitution, expectation, and reliance.
reliance damages are to repay the non-breaching party for any cost incurred in preparation towards completing their half of the bargain, because UT has not made any specefic monetary steps in providing Kiffin his job as opposed to any steps that would be required given any other coach this seems an unlikely avenue
expectation damages are to compesate the non-breaching party for any loss of expected profits caused by non-preformance of the contract. Because it is not provable the exact amount UT will lose (or possibly gain) from the contract being breached, expectation damages cannot be awarded. This is beacause of the fickle nature of athletics for profit endeavors that arise from the entertainment industry as a whole (which UT football is). See Kenford Co., Inc. v. County of Eire, 493 N.E.2d 234 (N.Y. Ct. App. 1986) (a perfect example of not being able to attach a specefic value to the expectation of profits and therefore cannot be awarded due to the breach of contract to build a new stadium). If UT were able to say they would have made an exact dollar amount from Kiffin not breaching down to the penny then they would be able to sue under this theory but as it stands now, UT is unable to recover.
Restitution damages are any damages that UT has paid to Kiffin towards their part of the contract that Kiffin would have failed to preform. These could include any salary paid for time after he left, not including any bonuses. Ut would be able to recover any salary they had paid him towards the future years in his contract.
The last would be liquidated damages that UT has already built into his contract commonly called a "buy-out" which UT has already or will receive.
So no, other than the buy-out already in his contract, UT would not be able to claim any damages from Kiffin's breach of contract under any theory of contract law.