Hi,
1.If we were to use the LPC54S016JET100 with a 1.8V Flash, can we program the flash through the SWD connection on the MCU, or do we need to use the bootloader?
>>>>>>Yes, you can program external spifi flash with SWD based on MCUXPresso tools, if it does not support the flash, you have to modify the *.cfx file.
This is the table the default spifi flash part number the current *.cfx supports.

For detailed inf, pls refer to the MCUXPresso_IDE_User_Guide.pdf located at:
C:\nxp\MCUXpressoIDE_11.8.0_1165
Secondly, you can download the flashloader to the RAM, using blhost tools to download via uart or usb in ISP mode.
Q2.Is there a power calculator available anywhere? I'll need to work out the size of our 1.8V supply.
>>>>>>pls download data sheet of LPC540xx from the link:
https://www.nxp.com.cn/docs/en/data-sheet/LPC540xx.pdf
and check the section 10.3 Power consumption for the power consumption for both core and peripherals based on clock frequency.
Hope it can help you
BR
XiangJun Rong