There doesn't seem to be any special significance to the specific foods mentioned. The impression I got from the scene is that the "four whole fried chickens and a Coke/dry white toast" are what Jake and Elwood regularly order, allowing Matt "Guitar" Murphy to realize they're in the diner before he steps out of the kitchen and sees them. In other words, their unusual eating habits act as a humorous calling card by which their bandmates/friends can recognize them.
Other than "announcing" their arrival, the order might also be considered a reflection of Jake and Elwood's personalities: the four fried chickens and Coke match Jake's reckless, disruptive nature, and the dry white toast matches Elwood's generally rather mild and low-key nature.
SOUL FOOD CAFE
ARETHA
Help you boys?
ELWOOD
You got any white bread?
ARETHA
Yes.
ELWOOD
I'll have some toasted white bread please.
ARETHA
You want butter or jam on that toast, honey?
ELWOOD
No ma'am, dry.
JAKE
You got any fried chicken?
ARETHA
Best damn chicken in the state.
JAKE
Bring me four fried chickens and a Coke.
ARETHA
You want chicken wings or chicken legs?
JAKE
Four fried chickens and a Coke.
ELWOOD
And some dry white toast please.
ARETHA
You all want anything to drink with that?
ELWOOD
No ma'am.
JAKE
A Coke.
ARETHA
Be up in a minute.
[She goes back to the kitchen.]
ARETHA
We got two honkies out there dressed like Hasidic diamond merchants.
MATT
Say what?
ARETHA
They look like they're from the CIA or something.
MATT
What they want to eat?
ARETHA
The tall one wants white bread, toast, dry, with nothing on it.
MATT
Elwood!
ARETHA
And the other one wants four whole fried chickens and a Coke.
MATT
And Jake! Shit, the Blues Brothers!
[Matt goes out into the cafe.]
Referred to copy of script here for the relevant dialogue.