The screenplay is useful in understanding what's going on. They're planning to travel deep into the Southern slaveholdings. Schultz is worried that this makes Django the potential target for any passing authority figure that takes it into his head to re-enslave him. He comes up with a brilliant solution. If they can't hide him, they can actively draw attention to him instead.
Dr.SCHULTZ: Still, seventy-five dollars in your back
pocket is a pretty nice grub steak, but it's
not going to get you very far in Greenville.
Not to mention a slave auction town in
Mississippi isn't the safest place you could
visit. Free or not.
DJANGO: I'll have my freedom papers.
Dr.SCHULTZ: Yes you will. But say you show them to some
rascals, and they take them from you and
tear them up?
Schultz chooses the clothes for Django and he reluctantly wears them.
Muddy and wet big city Chattanooga. We're in the back of a STORE that
.sells SERVANT/HOUSE NIGGER UNIFORMS. Django comes bursting out of the
stores back door. He's very distressed. One glance at the outfit he's
wearing explains the distress.
DJANGO is dressed in a powder blue satin Little Lord Fauntleroy outfit, that
wouldn't be out of place in the court of Marie Antoinette at Versailles.
Dr.Schultz comes trailing after him.
Dr.SCHULTZ: Django, you have to, it's part of "The Act".
You're playing a character. Your character
is The Valet. This is what The Valet wears.
Remember what I told you. During the act,
you can never break character.
This ruse is successful. His outfit is so garish and eye-catching that it essentially defies belief that anyone other than a free man (albeit one that wants to keep his job around an eccentric wealthy employer) would choose to wear clothes like that. Anyone who sees him, their first question won't be "is that an escaped slave?" it'll be "what the hell is that man wearing!?" which gives Django (and Schultz) more scope to respond.