Seems a little clunky, I think you have to have ten set up before any would get "removed".
If you click on one of your custom colors (example #22ffcc) that's the selection, and it goes to the front of the third row. If you like that color, leave the hexadecimal color code in the settings as is.
If you have another custom color set up, you can click on that, and it becoms the selection and goes to the front of the third row.
If you change the color code in the settings, it will become one of your new custom colors.
Semi related, Imgflip updated the site 2019-05-17 how user specified colors are stored. Now 3,4,6 & 8 character hexadecimal colors codes work, previous to that date only 3, 4 or 6 character codes were supported.
https://en.m.wikipedia.org/wiki/Web_colors
Basically what that means is transparency is also supported now for all the usual colors when you use 8 characters where the usual 6 character color code goes. Right now you have manually enter an 8 character color code, that might change if the Imgflip color picker is updated with a second slider or something like that.
The last two characters of an 8 character color code specifies 256 levels of transparency, 00 is fully transparent, ff is fully opaque.
I sometimes use an eight character yellow color code (with transparency) when I'm drawing on a meme, kind of like using a highlighter.
Example #eeee0077 or
#eeee0033