easiest airport to fly out of from South Kensington

You can take the Picadilly line direct to Heathrow, that seems like the easiest.

I would recommend Gatwick- South Kensington is only two stops on the Circle or District line away from Victoria, and from there you can get the Gatwick Express train directly to Gatwick, which takes half an hour. They run every 15 minutes. Personally I would arrive between 1.5 - 2 hours before your flight (if checking luggage two hours, if not, I find 90 mins is plenty).

You can find the Gatwick Express timetables here, and if you book online in advance it's generally a bit cheaper: https://www.gatwickexpress.com/

Good luck with your planning!

Personally, I’d go for Heathrow.

But if you go from Victoria, go by Southern Trains - not the Gatwick Express- it takes 3 minutes longer but it’s noticeably cheaper.

Heathrow. 40-45 minutes direct on the Piccadilly line.

Arrive 2 hours ahead in case the line at security is long.

39 minutes from So Ken to Heathrow 2/3 on the Piccadilly, no change.

33 minutes on the Southern train to Gatwick and 10 minutes to change at Victoria if you know your way including getting upstairs, and 4 minutes on the Circle and District to Victoria fro, So Ken, is about 47 minutes or so.

Easiest? No change beats one change and a walk. Fastest, because of no change, Heathrow. T4 or T5 is a few minutes longer.

So you pays your money and takes your choice.

I’m going to disagree with the comments above and recommend London City airport. The journey from South Kensington is as quick or quicker than to Heathrow or Gatwick. Admittedly it will involve two changes, at Westminster and Canning Town, but only takes 40 minutes.

But the real benefit is how much quicker, easier and nicer it is to transit LCY than any other London airport. The time needed is much less.

The only real stumbling block is that, because it’s better fares might be more expensive. But I would pay quite a premium to fly from there.

I'm going to add an additional consideration which is if you have a lot of luggage, that is much easier to deal with on a train vs the tube (if you are travelling light it doesn't really matter). You are also more likely to get a seat on the train vs tube although that is also dependent on time of day. Gatwick would still be my personal choice but as long as you don't choose Luton or Stansted it's not a huge difference and might be better determined by the price of the flights.

Which London to Dublin airline are you flying on? That may make a difference which airport. Are you choosing your flight by airport or by airline?
In July I am flying on Aer Lingus. But I am going to Heathrow from Bath late afternoon, staying overnight at LHR hotel, then flying to Dublin the next morning and going elsewhere in Ireland upon arrival.

horsewoofie (above) - there was no need to go from Bath to Heathrow in order to fly to Dublin as you could have taken a shuttle bus the short distance from Bath to Bristol Airport to fly to Dublin and saved yourself a pile of money.
https://www.bristolairport.co.uk/to-and-from-the-airport/by-bus-and-coach/