I wish to find the quickest way from Notting Hill to City airport by train or by taxi or Uber. I have bags.
The quickest way will undoubtedly be by London Underground and DLR. The simplest and also quite cheap route is to travel from Notting Hill Gate station on the Central Line to Bank, where you can change onto the DLR to reach London City Airport. (If you REALLY want the absolute cheapest you can head West from Notting Hill Gate via Shepherd's Bush, the London Overground to Stratford, and the DLR from there, avoiding Zone 1, for a fare of £1.70 peak/£1.50 off-peak, but this will take much longer).
However, both Notting Hill Gate and Bank central line stations require the use of staircases. At Bank you can avoid escalators and get a lift to the DLR but must still use stairs to exit the central line platform; at Notting Hill Gate it appears you must use both stairs and escalators. If you are able to carry your bags up and down short flights of stairs and on escalators, then this will likely be the quickest and easiest route for you. This journey will cost £3.30 if you travel in the peak time, or £2.80 off-peak, if you pay with an Oyster card, contactless payment card, or contactless mobile pay.
If this sounds too difficult, fear not! Instead you can get a bus, taxi, or minicab (eg Uber) to Green Park or Bond Street station, where there are lifts. From here travel on the Jubilee Line to Canning Town, which also has lifts, and catch the DLR there on to London City Airport. The price for the tube/DLR portion will be the same as above; the price for the bus would be £1.50, and the price for a taxi or minicab I have no idea.
London City Airport DLR station has lifts.
The TfL Journey Planner allows you to specify escalators rather than stairs, or entirely step-free journeys if you wish.
I have bags
As noobservergirl points out, the obvious route from Notting Hill Gate to London City Airport is the Central Line to Bank, then the DLR to London City Airport.
The trouble is that while the DLR is modern enough to have lifts and level access throughout, the Underground is still mostly stuck in the Stone Age accessibility wise, with no lifts available to the Central Line platforms at either Notting Hill Gate, or Bank. So the question is: are your bags small/light enough that you can manage them on the long escalators of the Underground?
Another option that is a bit slower, but might be worth considering if you have to travel with larger bags, is to take a taxi/private hire to Shepherd's Bush. From there you can pick up an Overground service to Stratford and then the DLR to London City Airport. According to the map there is level access to the Overground platforms at both Shepherd's Bush and Stratford.
If taking the Stratford route on Oyster/contactless then you should touch a pink reader at Stratford to ensure you are charged the correct fare.
46 mins using underground via central line from Notting Hill Gate, and then change onto the DLR at Bank station. If you're heading during off-peak hours (ie early in the morning or late in the evening), then there will be less traffic but I would predict it would be a slightly shorter journey.
I use the CityMapper app. It gives you estimated timings using different modes of transport within London. Going by Uber /Car is around a 1hr journey time apparently
42 minutes if you do this:
From Notting Hill Gate underground station, take the CENTRAL line terminating at Loughton to BANK station.
From BANK, switch to DLR terminating at Woolwich Arsenal. London City Airport is 10 stops from Here.
The number of bags, as well as the time you are travelling, will eventually determine if you should use Uber or not. If you are going during peak period and you have lots of bags, it may not be worth it using the train as it may be overcrowded and you may have nowhere to stand or sit. I hope that helps