How long will it take to for the belly button to heal after a tummy tuck?

All incision healing follows a timeline: first week, communication and clean-up between the edges; second week migration of fibroblasts and beginning of laying down of collagen.  At this time there is some tensile strength and wounds do not come apart if they have a deep layer closure. After two weeks the skin edges are joined well enough that you would not have an opening unless you pulled purposely and even then it would be difficult. Tensile strength builds up progressively and is about maximum at twelve weeks.
 Scar starts forming after three weeks, and from three to eight weeks, if an abdominal incision is protected from tension with something like Embrace, or a good deep layer closure that takes tension off the skin, the best possible scar quality in terms of flatness, narrowness can occur.
Belly buttons are the same, but have particular problems: since they are often done as a continuous unbroken circle or oval, contraction along the entire length of the scar can occur.  I had to correct a pinhole umbilicus this week as the circumference had completely contracted and hidden the belly button skin.  Sometimes, depending on genetics, the scar tendency is pronounced and a hypertrophic scar (red, raised, thick, discolored) develops in the belly button, incision scar, or both.
If this occurs, then several things can be done. Time alone will sometimes result in a more pliable softer scar, but if this doesn't seem to be happening after 4-6 months, steroid (kenalog) can be injected to soften the scar. This sometimes has a trade-off of thinning normal skin around, or lightening it. Sometimes our fractional, Lux 1540, erbium scar laser helps to soften and flatten the scar.  We may also alternate that with microneedling with or without platelet rich plasma.
Finally, it seems that after a year, when there is much less tension on the skin than at the time of the initial closure, a scar revision (cutting out the old scar and stitching together) results in a normal, unscarred incision. Conservatively, I usually do that either in segments or half at a time, or just the bad parts of the scar.  This technique also seems to work well when revising the bad scars that sometimes occur under the breast after breast lifts or reductions.

belly buttons heal at the same pace your tummy wound heals.  You should be asking your surgeon if you have any concerns about how you are healing.

Healing starts immediately after surgery and depending on your body and quick of a healer you are the healing time can range anywhere from 2 weeks to several months. Try and eat a lot of protein to promote healing quicker. Follow all your doctors instructions and you should be fine.
Dr. Quintero