What are the pros and cons of gifting RSUs to a 22 year old son? Will he have to pay tax for the gains I made before transferring to him? Does he have to pay kiddie tax?

Yes, your son will be liable for any capital gains tax due when he sells the gifted stock.  This FAQ explains how he will determine the stock's cost basis when he sells it:  https://ttlc.intuit.com/questions/3353068-how-do-i-determine-the-cost-basis-of-stock-i-received-as-a-gift

Your cost basis is the market value of the shares on the day they vested to you.  So when your son sells he'll need to know that number, as well as their market value on the date of the gift.

This TT FAQ explains the ins and outs of the Kiddie Tax, and should answer your question about that:  https://ttlc.intuit.com/questions/1900671-what-is-the-kiddie-tax

Note too that, if the value of your gift (on the date of the gift) exceeds $15,000 (2018), you must report the gift to the IRS using Form 709.  There is a lifetime exemption of $11.4 million, so it is extremely unlikely any gift tax will actually be due - but gifts over $15,000 must still be reported by the donor.  https://www.irs.gov/pub/irs-pdf/f709.pdf

Thank you so much TomD8! Very helpful. I am slightly confused about the article in the 1st link. In my case, the FMV when I gift it to my son would be more the original cost basis. For e.g. if the value was a) $100 they vested for me, b) FMV is $150 when I gift to my son, and c) the value becomes $175 when he sells them: Would he also have to pay the tax for the $50 gain that happened when the stocks were with me, or will he only pay the tax on the $25 gain after he received them, or will he have to pay the tax on $75 for the entire time after vesting? Sorry that I didn't understand..

In your scenario he would owe tax on the entire $75 gain.  At the time of the gift he acquired your original cost basis of $100.  His capital gain would be long term (and taxed at a lower rate) if he sold the stock more than a year after your original vesting date.  (Note that the 2019 long term capital gains tax rate is 0% for single taxpayers whose taxable income is $39,375 or less.)
If he sold the stock less than a year after your original vesting date, his gain would be taxed as ordinary income according to his tax bracket.

Thanks a lot TomD8! Super helpful! My stocks vested more than a year ago, so I understand that him or me won't have to pay any tax if he sold them right away. The only other worry I have is: He is only 22.. so would he have to pay any Kiddie tax if he sold them as soon as I transfer to him now and not wait until he is 24? Thanks again.

This IRS reference explains who must pay the Kiddie Tax.  It also explains the circumstances when a parent may report the income on their own tax return:  <a rel="nofollow" target="_blank" href="https://www.irs.gov/taxtopics/tc553">https://www.irs.gov/taxtopics/tc553</a>

Thanks again TomD8.. Just 1 minor clarification: Does the $39,375 income you mentioned include the gains from the stocks or only his salary? For example, if the gain from the stocks I transfer to him is $50k, but he has no income as he is only a student, then his tax on the gains from the stocks transferred would still be zero, right? Thanks so much again.

Yes, the capital gain is included in the income used to figure out what tax rate applies to the capital gain.