Here's what you need :

1- A way to take screenshots / Screenshot a specific part of your screen (Snipping tool should be good enough)

2- A software / website with the ability to pick colours from images as well as showing the colour code of said picked colour (You'll have to look for this one but i assume most photo editing websites/software allow you to do this)

What you need to do :

1-Get a close up picture of your character wearing the piece of clothing that you want to colour (This is to prevent any possible variance in colours due to compression)

2- Use that picture you took in the software/website you desire and pick the colour of the part you want to edit

3-Go back to starbound, Click on the + sign (It says add colour when you hover over it)

3.5- The left side's colour code (The editable box that contains numbers and letters) is the target colour, Aka the colour we want to modify, The right side's colour code (The editable box that
contains numbers and letters) is the destination colour, Aka the colour we want the part to be.

4-Replace the target colour code with the one you got from step 3

5-Get the colour code of the colour you wish to replace the old one with and replace the destination colour code with it. Or use the colour picker to get the colour you wish and click on 'set dest'

6- Repeat from step 2 depending on how many colours you wish to replace, Keep in mind that you'll probably need to re adjust the destination colour multiple times due to colours not looking too good on your first adjustment.

Enjoy :3