Each of these in an indicator or either fluid that is lacking proper friction properties, or low control pressures - at least in the majority of cases. The problem is the "why" and each case needs to be individually analyzed.
A shudder is a jerky feeling.... usually occurs as you are accelerating and change gears. Shudder originates at the fluid interface between two parts (like a band and drum, or a wet clutch steel and friction - often times it is in the Torque Convertor clutch!). Sometimes the fix for a shudder can be as easy as a fluid change. As I noted, shudder can also occur because the lockup of the parts referenced is not occurring strongly enough, fast enough. (Low pressure). The 5R55E needs Mercon V and if you try Mercon III for example you WILL get a shudder.
A flare is when the transmission changes gears and the engine rpms will run up a little like the gear change and lockup in the new gear has occurred too slowly. This is generally either related to pressure, or the timing of the gear change - controlled by the Valve body and engine computer. The 5R55E is notorious for a slight 2-3 flare, even in "good" trannies. Here is a graph of rpm's on the input shaft showing the 2-3 flare (Graph courtesy of Allbert)
The flare here is about 75-100RPM and relatively brief, not a big deal and as I said common in the 5R55E's. Look at the next shift point... NO flare.. Really noticeable flares can be several hundred RPM's.
A slip is when your transmission has a component that is not fully locking up... the vehicle speed will not increase at the same rate the rpm's increase when you step on the accelerator. Of the 3, a slip has the most potential for causing transmission damage, and can produce tremendous damaging heat. A slip may start because of pressure issues or some other problem, but once the friction materials become "glazed" you may be past doing anything but repairing them (can you say "teardown?"). Glazed frictions just will not hold like good ones will.
Hope that helps.