Some would call flaring, slipping. Its is not! The term refers to an increase in rpms during the shift as if there was slippage.
To understand flaring one must understand a little about how auto transmissions work and the term shift overlap.
Because in the mechanical world absolutely nothing moves instantly, shift timing must be part of the design concept. In the case of fourth gear a band is released and a clutch is activated. The end result is that all the guts of the trans are locked as one and spin together making high gear. As it turns out it takes very little time to release a band. Applying the clutch is a different matter; there is a stack of discs that must be squeezed together to apply. This takes a finite amount of fluid and has an exact fill rate due to oriface size and original freeplay of the pack.
The problem occurs in this tranny when the piston causes a fluid loss and the clutches are wore or the seal is leaking in the pack or in the case of early cars the clutch packs were assembled with too much play. Now what happens is the band releases which was holding the outside of the clutch drum stationary related to the trans case. This caused a gear reduction as the output came off another element of the planetary gear set (much too hard to explain with words - need a picture). Anyway at the moment of release the group is able to freewheel and the engine is unattached and revs. Normally the release action is retarded and the clutch fill action is early engaged to give what is called shift overlap or shift timing. In theory both items are applied at the same time. Sort of like "just in time" inventory control the clutch which is started to engage first gets there just in time that the engine is normally not released - no flare.
Wear in the pack and fluid losses both in the piston and clutch seals changes the timing equation and causes this problem not slipping.
Bosch Master, ASE Master, L1
33 years MB technician