Can you tell me who's talking...
...and what is she trying to tell us?
No maths needed
After the "dirty job" made by Gareth, the solution of this puzzle should be really close
Not really an answer but (too large to fit in a comment and) may save others some scutwork: OP says that "the lack of a text transcription is intentional" but if this puzzle is mostly about looking up RGB colours on the internet then that is No Fun and I'd like to save other people the bother.
Of course it may turn out that none of this has anything to do with the actual puzzle and I've saved people some pointless bother, but actually that's even better.
B3 44 6C | C8 A2 C8 | 6E AE A1 | 72 74 72 | F4 F0 EC | E9 D6 6B | E9 D6 6B | 87 A9 6B E9 5C 4B | E9 96 7A | 72 2F 37 | FF 99 33 | ED 91 21 | 99 66 CC | DB D7 D2 | 96 71 17 3F 00 FF | 56 82 03 | 4C 51 6D | DF 73 FF | 3F 00 FF | 72 74 72 | F0 FF F0 | E9 FF DB 72 74 72 | FF FF 00 | 48 3C 32 | F1 9C BB | 54 5A A7 | FF AE 42 | FC F7 5E | 80 00 20 C1 9A 6B | DE AA 88 | F4 00 A1 | F0 EA D6 | 15 60 BD | D8 BF D8 | 39 FF 14 | D4 70 A2 B2 EC 5D | 3F FF 00 | FD F5 E6 | 5F 8A 8B | E9 FF DB | 3F FF 00 | 00 74 74 | 9E 5E 6F ED 87 2D | 5A 4F CF | C0 80 81 | F0 FF F0 | F2 85 00 | AB 4B 52 | 4B 00 82 | 87 FF 2A 63 51 47 | E9 FF DB | 00 80 00 | FF 99 66 | E4 D9 6F | FF FF FF | DF 73 FF | FF 68 1F
Names, according to Some Website Or Other:
Irresistible | Lilac | Green Sheen | Nickel | Isabelline | Arylide yellow | Arylide yellow | Asparagus
Fire opal | Darksalmon | Puce red | Deep saffron | Carrot orange | Amethyst | Timberwolf | Bistre brown
Electric ultramarine | Avocado | Independence | Heliotrope | Electric ultramarine | Nickel | Honeydew | Nyanza
Nickel | Yellow | Dark lava | Amaranth pink | Liberty | Yellow Orange | Icterine | Burgundy
Camel | Tumbleweed | Fashion fuchsia | Eggshell | Denim | Thistle | Neon green | Wild orchid
Inchworm | Harlequin | Oldlace | Steel Teal | Nyanza | Harlequin | Skobeloff | Rose Dust
Cadmium orange | Iris | Old rose | Honeydew | Tangerine | English red | Indigo | Spring Frost
Umber | Nyanza | Green | Atomic tangerine | Straw | White | Heliotrope | Orange-red
Nothing leaps out at me on looking at any of the above, but I haven't looked very hard.