Oozing sap, termed gummosis, can be caused by a few different factors, and they can be hard to tell apart since there is often little other outward indication of the problem until it's progressed significantly. Wood-boring insects, fungal or bacterial infections, and general stress or tree injury can all cause gummosis. Neither a borer nor a pathogen could be treated, though, since they are beyond the reach of pesticides at that point and even a successful treatment wouldn't reverse any existing damage to the vital sapwood. All you can do for now is to monitor the tree for watering needs and canopy dieback (something that may have to wait for spring since they're shedding leaves soon) and trim out dead branches. Sources of tree stress could be due to root moisture -- either too much (which cherries are notoriously intolerant of) or too little (before our recent rains), perhaps tied to the limited root zone due to the nearby pavement coupled with the root competition from the Vinca groundcover. (If you do need to remove this tree at some point, we suggest replacing the Vinca as well, since it's an invasive species here.)

You can explore our ornamental cherry diagnostic page for more detail. The Kwanzan cherry isn't necessarily at risk if it's not very stressed, since many of these pests and pathogens are opportunists, targeting weakened or injured trees (trunk cuts, improperly pruned branches, etc.). Make sure no added influx of water is reaching the trees, such as from a nearby roof downspout outlet that may need redirecting, and feel the soil about six inches deep in the root zone to determine when they need irrigation. (In general, summer through fall as the weather dictates; when it's becoming relatively dry to the touch at that depth, water thoroughly.)

If this tree succumbs and is removed, you can do a post-mortem of sorts to try to narrow-down what caused the gummosis. It's possible more than one issue overlapped, so you may find both borers and infection. Borers chew a tunnel into the wood and if they aren't plainly visible when the trunk is cut apart to investigate, their frass (insect poop) mixed with some sawdust in those chambers will be. Infections, on the other hand, tend to stain wood a darker color and may be present either in the wood just under the bark or more into the interior heartwood. If neither tunneling nor staining is evident, perhaps environmental conditions caused root dieback instead.

Miri