you probably could just loop that variable to send it like

Code (Text):

1.         if {bloodlust::*} contains player's uuid:
2.             loop {bloodlust::*}:
3.                 send "&6Faction: &f%player%: %arg-2%" to loop-value
4.         else if {vanguard::*} contains player's uuid:
5.             loop {vanguard::*}:
6.                 send "&6Faction: &f%player%: %arg-2%" to loop-value

but.. i would do it like this just saying i've edited your skript a little

Code (Text):

1. on chat:
2.     if {TeamChat.%player%} is true:
3.         if {bloodlust::*} contains player's uuid:
4.             loop {bloodlust::*}:
5.                 send "&6Faction: &f%player%: %message%" to loop-value
6.         else if {vanguard::*} contains player's uuid:
7.             loop {vanguard::*}:
8.                 send "&6Faction: &f%player%: %message%" to loop-value
9.  
10.  
11.  
12.  
13. on quit:
14.     remove player's uuid from {bloodlust::*}
15.     remove player's uuid from {vanguard::*}
16.     delete {team.%player%}
17.     delete {TeamChat.%player%}
18.  
19. command /faction [<text>] [<text>]:
20.     trigger:
21.         if arg-1 is "join":
22.             if {team.%player%} is not set:
23.                 if arg-2 is "bloodlust":
24.                     if {first.faction.%player%} is true:
25.                         set {team.%player%} to true
26.                         add player's uuid to {bloodlust::*}
27.                         set {first.faction.%player%} to false
28.                         set {cant.move.%player%} to false
29.                         send "&6Faction: &fJoined the &cBloodlusts &fteam!" to player
30.                     else:
31.                         send "Error: You're already in a faction!" to player
32.                 if arg-2 is "vanguard":
33.                     if {first.faction.%player%} is true:
34.                         set {team.%player%} to true
35.                         add player's uuid to {vanguard::*}
36.                         set {first.faction.%player%} to false
37.                         set {cant.move.%player%} to false
38.                         send "&6Faction: &fJoined the &9Vanguard &fteam!" to player
39.                     else:
40.                         send "Error: You're already in a faction!" to player
41.         if arg-1 is "chat":
42.             if {first.faction.%player%} is false:
43.                 if arg-2 is set:
44.                     if {bloodlust::*} contains player's uuid:
45.                         if {TeamChat.%player%} is true:
46.                             send "&6Faction: &fChat Mode &4Disabled" to player
47.                             set {TeamChat.%player%} to false
48.                             stop
49.  
50.                         set {TeamChat.%player%} to true
51.                         send "&6Faction: &fChat Mode &2Enable" to player
52.                     else if {vanguard::*} contains player's uuid:
53.                         if {TeamChat.%player%} is true:
54.                             send "&6Faction: &fChat Mode &4Disabled" to player
55.                             set {TeamChat.%player%} to false
56.                             stop
57.  
58.                         set {TeamChat.%player%} to true
59.                         send "&6Faction: &fChat Mode &2Enable" to player
60.                     else:
61.                         send "&cError: You aren't in a faction"
62.  
63. command /factionblood:
64.     trigger:
65.         send "%{bloodlust::*}%" to player
66.  
67. command /factionvangu:
68.     trigger:
69.         send "%{vanguard::*}%" to player

just basicly put the chat feature in a chat event