Pulse the Captain Crunch cereal and the cornflakes in a blender or food processor until they form fine crumbs; transfer to a shallow bowl.
In a second shallow bowl, whisk the eggs and milk together until combined.
In a third shallow bowl, combine the flour, granulated onion, granulated garlic, and ground black pepper.
Set up a dredging station: coat each chicken tender first in the egg mixture, then lightly in the flour mixture, and finally press into the cereal crumbs to fully coat.
Heat vegetable oil in a deep-fryer or large deep skillet to 325°F (about medium-high); there should be enough oil to fully submerge the tenders.
Fry the coated chicken tenders in batches for 3 to 4 minutes each, until golden brown and the internal temperature reaches 165°F.
Use tongs to transfer the cooked tenders to a paper towel-lined plate to drain, then serve immediately with Creole mustard.