Have you fully read my flashing guide?
I have a lot of pictures and info there. Also info about and various solutions for handling the two grounds.
The table containing the solder points is from that guide, so it looks like you’re well on your way.
I’m not 100% sure what you mean by “connected the 2 pins in 3V”.
If you mean that you put the 3.3V versus 5V jumper to the 3.3V setting, then this is exactly what you need. That is what I see on your photo too, so that is fine.
You can use the two GND holes for connecting to GND and GPIO0 on the device. That is okay. If you solder the GPIO0 wire to GND, then beware that the device will always boot in flashing mode when the serial adapter is connected. Therefore, it might be best to connect GND to a GND hole on the adapter, but use a wire with a connector to connect GPIO0 to the GND pin on the adapter. That way you can easily disconnect GPIO0 from GND, allowing you to use the adapter for example for getting serial logging.
Do not connect anything to the 3.3V hole. The 3.3V that is mentioned in the table, indicates that the serial adapter should use 3.3V (and not 5V) for sending signals to the RX pin on the lamp. It does not mean that 3.3V must be connected to it.This is what dictates the use of the voltage jumper on 3.3V on the serial adapter.
The TX on the lamp must be connected to RXD on your serial adapter
The RX must be connected to TXD
Note that these two are also available as pins that you can use a wire with a connector for. Either the hole or the pin is okay. The exact pinout of the pins is written on the serial adapter board, but with these it can be hard to see because the 3.3V/5V jumper is a bit in the way.
Don’t use RXL and TXL, because those are used for status LEDs to indicate when there’s dat being sent over the lines (hence the “L” in their name).
When soldering the RXD/TXD holes, then the layout would probably be best like this:
So with the GPIO0 to GND connection done in a way so it can be detached.
I use a Windows10 laptop myself for flashing, using the Esphome-Flasher tool.
I hope this helps!