My uncle wants to make a donation to our kid's college fund. What's the maximum allowed per year (tax-free) and how many years can be combined on a single donation?

Is it a 529 plan? Which state is the fund established in?

We are currently evaluating what's the best option. The 529 is established in IL. We understand, he can contribute up to $70,00 (prorated over a 5 year period) without incurring into the gift tax, but how about the recipient? If he was to make a contribution to an alternative savings account, will he (or us) be subject to the $14K max annually? I understand for those alternative options, you can't combine multiple options without being taxed. Appreciate your help!

No. Neither the beneficiary of the account (the child) or his parents report anything about the uncle's  contribution/gift on their tax return. Gift recipients do not file a gift tax return; only the giver.
The Uncles gift does not affect the parents ability to contribute to other accounts or even the same 529 that the Uncle gives to.. The $14,000/$70,000 limit is per individual giver

Essentially, there is no federal IRS limit to the amount. It can all be done in one year or multiple years. There is no federal deduction for making a contribution. States may have a limit ($300,000) and most states allow a deduction for a contribution and the Uncle gets the deduction even though the child is not his dependent. The state deduction is limited (see http://www.savingforcollege.com/compare_529_plans/index.php?page=compare_plan_questions&plan_question_ids[]=437&order_by=plan_question_437 ) but there is usually a roll over provision.

In a sense there is a federal limit of $70,000 to avoid a gift tax return. But, "Gift Tax" is somewhat of a misnomer.  Even though a gift tax return may be required, very few people ever actually pay federal gift tax. The purpose of the gift tax return is usually only to document a reduction in the allowable estate tax exemption.
See https://turbotax.intuit.com/tax-tools/tax-tips/Tax-Planning-and-Checklists/The-Gift-Tax-Made-Simple/INF12127.html

Reference: https://us.axa.com/goals/saving-for-college/articles/529-plans-contributions-withdrawls.html

Hal_Al, thank you for the thorough response! In either case, do we "as recipients" have to declare this gift as "income" if it is not under a 529 plan?

Gifts are not income and are not reported on the recipient's  income tax return. You (the parents) are not the recipient of a gift; the child is.