If the black is chippy or cracked, can you get your hands on a pressure washer? (Very difficult to sand wicker.) You have to be very careful with PW. Best done in hot weather, so depends on where you live. I had a wicker table with chippy paint. Pressure washer (gently used) got nearly all of it off. Get too close and you will have split fibers. I let it dry in the sun well for several days. Primed with rustoleum spray primer, then sprayed with rustoleum finish coat. Has held up pretty well for nearly 4 years now, no chipping/flaking yet. (It's outside on my deck, covered for winter, and covered in summer when storms or rain is imminent.

If the black enamel is intact, no chips, then wipe it down with Dirtex or another good pre-paint cleaning solution. (If in doubt, ask in the paint forum here.) Use a good oil-based primer. (I like Zinsser products, or Kilz might be a good option to hide that black). Then pain with your white enamel.

A decent primer/undercoat. There may be one specifically available for coverage. I would also suggest using an airless sprayer, trying to brush wicker would be entering a world of pain.

If you think you'd have the use for it, you can get something like a Wagner paint crew for Kilz does seem to be a good product.

ditto the priming - on the wicker, a coat of gray automotive primer would make a good barrier coat, on the wood, I'd go with two coats of Killz or other brush-on primer.

thinning the paint slightly, and using a 'loose' brush that you're not going to miss when it dies, lets you 'scrub' the paint into the weave of the wicker easier - spraying is 'easier' but I'm not one of the lucky people who has ever gotten an airless sprayer to work properly, so it's been a moot point for me.