Color and Texturizer
A: Provided the formulas of the texturizer and hair color are compatible and your hair is in proper condition, you could have one service follow another.
Especially considering that the hair coloring for an African-American client will more likely include lightening the hair's natural color, the processes can be very harsh on the hair.
Giving the hair's cuticle layer time to relax and re-conform along the hair shaft is a good idea and will help to lessen the risk of damage caused by strong chemical processing.
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See also:
Do you think using relaxer and color at the same time is a bad choice?
What would you suggest that I use to color my hair that is safe?
The scientific processes during perming & relaxing
The special needs of African-American hair