Blue duck, red duck, gray duck

LuaLaTeX, 220 211 characters

command:

lualatex -interaction nonstopmode

Not the shortest, but the fanciest. Based on @skillmon's solution

\RequirePackage{tikzducks}\newcount\b\let~\def~\0{red}~\1{orange}~\2{yellow}~\3{green}~\4{blue}~\5{cyan}~\6{violet}~\7{gray}\loop\b\uniformdeviate8\tikz\duck[body=\csname\the\b\endcsname]; \ifnum\b<7\repeat\stop

6502 machine code (C64), 124 bytes

00 C0 AD 12 D0 85 02 A2 17 8E 18 D0 A5 02 F0 03 0A 90 02 49 1D 85 02 A8 CA 10
02 A2 2F BD 42 C0 D0 F6 88 D0 F3 86 FB E8 BD 42 C0 F0 06 20 16 E7 E8 D0 F5 AA
BD 73 C0 F0 06 20 16 E7 E8 D0 F5 A6 FB D0 C9 60 00 C7 52 45 59 00 D2 45 44 00
CF 52 41 4E 47 45 00 D9 45 4C 4C 4F 57 00 C7 52 45 45 4E 00 C2 4C 55 45 00 C9
4E 44 49 47 4F 00 D6 49 4F 4C 45 54 00 20 44 55 43 4B 0D 00

Online demo -- Usage: SYS49152.

---

Explanation (commented disassembly):

         00 C0       .WORD $C000        ; load address
.C:c000  AD 12 D0    LDA $D012          ; current rasterline as seed
.C:c003  85 02       STA $02            ; to "random" value
.C:c005  A2 17       LDX #$17           ; cfg for upper/lower, also use as
.C:c007  8E 18 D0    STX $D018          ;    initial index into colors array
.C:c00a   .loop:
.C:c00a  A5 02       LDA $02            ; load current random val
.C:c00c  F0 03       BEQ .doEor         ; zero -> feedback
.C:c00e  0A          ASL A              ; shift left
.C:c00f  90 02       BCC .noEor         ; bit was shifted out -> no feedback
.C:c011   .doEor:
.C:c011  49 1D       EOR #$1D
.C:c013   .noEor:
.C:c013  85 02       STA $02            ; store new random val
.C:c015  A8          TAY                ; use as counter for next color string
.C:c016   .findloop:
.C:c016  CA          DEX                ; next char pos in colors (backwards)
.C:c017  10 02       BPL .xok           ; if negative ...
.C:c019  A2 2F       LDX #$2F           ;    load length of colors - 1
.C:c01b   .xok:
.C:c01b  BD 42 C0    LDA .colors,X      ; load character from colors
.C:c01e  D0 F6       BNE .findloop      ; not zero, try next character
.C:c020  88          DEY                ; decrement random counter
.C:c021  D0 F3       BNE .findloop      ; not zero, continue searching
.C:c023  86 FB       STX $FB            ; save character position
.C:c025  E8          INX                ; increment to start of color
.C:c026   .outloop:
.C:c026  BD 42 C0    LDA .colors,X      ; output loop for color string
.C:c029  F0 06       BEQ .duckout
.C:c02b  20 16 E7    JSR $E716
.C:c02e  E8          INX
.C:c02f  D0 F5       BNE .outloop
.C:c031   .duckout:
.C:c031  AA          TAX                ; A is now 0, use as char pos for duck
.C:c032   .duckoutloop:
.C:c032  BD 73 C0    LDA .duck,X        ; output loop for duck string
.C:c035  F0 06       BEQ .outdone
.C:c037  20 16 E7    JSR $E716
.C:c03a  E8          INX
.C:c03b  D0 F5       BNE .duckoutloop
.C:c03d   .outdone:
.C:c03d  A6 FB       LDX $FB            ; load saved character position
.C:c03f  D0 C9       BNE .loop          ; not zero -> continue main loop
.C:c041  60          RTS                ; zero was start of "Grey" -> done
.C:c042   .colors:
.C:c042  00 c7 52 45    .BYTE 0, "Gre"
.C:c046  59 00 d2 45    .BYTE "y", 0, "Re"
.C:c04a  44 00 cf 52    .BYTE "d", 0, "Or"
.C:c04e  41 4e 47 45    .BYTE "ange"
.C:c052  00 d9 45 4c    .BYTE 0, "Yel"
.C:c056  4c 4f 57 00    .BYTE "low", 0
.C:c05a  c7 52 45 45    .BYTE "Gree"
.C:c05e  4e 00 c2 4c    .BYTE "n", 0, "Bl"
.C:c062  55 45 00 c9    .BYTE "ue", 0, "I"
.C:c066  4e 44 49 47    .BYTE "ndig"
.C:c06a  4f 00 d6 49    .BYTE "o", 0, "Vi"
.C:c06e  4f 4c 45 54    .BYTE "olet"
.C:c072  00             .BYTE 0
.C:c073   .duck:
.C:c073  20 44 55 43    .BYTE " duc"
.C:c077  4b 0d 00       .BYTE "k", $d, 0

Perl 5, 79 bytes

say$_=(Grey,Red,Orange,Yellow,Green,Blue,Indigo,Violet)[rand 8]." duck"until/y/

Try it online!