C-Flex is a Philips-Respironics brand-specific term for CPAP Exhalation pressure relief.
According to the Philips-Respironics website: "C-Flex pressure relief technology makes sleep therapy more comfortable by reducing pressure at the beginning of exhalation and returning to therapeutic pressure just before inhalation. The level of pressure relief varies based on the patient’s expiratory flow and which of the three C-Flex settings has been selected." 
C-Flex Comfort Feature (from SystemOne_REMstar_Auto_Domestic_English_Provider_Manual.pdf)
The device consists of a special comfort feature called C-Flex. When C-Flex is enabled, it enhances patient comfort by providing pressure relief during the expiratory phase of breathing. In the diagram, the dashed line represents normal CPAP therapy in comparison to the bold line representing C-Flex. C-Flex levels of 1, 2, or 3 progressively reflect increased pressure relief. C-Flex pressure relief is determined by the C-Flex setting and the amount of patient flow. C-Flex returns to the set pressure by the end of exhalation, when the airway is most vulnerable to closure.
Note: The patient also has access to this setting, if C-Flex is enabled
A-Flex (C-Flex+) Comfort Feature
The device consists of a special comfort feature called A-Flex if Auto-CPAP therapy is enabled (or C-Flex+ if CPAP therapy is enabled). When A-Flex (C-Flex+) is enabled, it enhances patient comfort in three ways:
1) by smoothing the transition between the end of inhalation and the beginning of exhalation,
2) by providing significant pressure relief during the beginning of exhalation, and
3) by reaching an end exhalation pressure of no more than 2 cm H2O below the high point of inspiration.
In the diagram, the dashed line represents CPAP pressure in comparison to the bold line representing A-Flex (C-Flex+). A-Flex (C-Flex+) levels of 1, 2, or 3 progressively reflect increased pressure relief during the beginning of exhalation.
With A-Flex (C-Flex+), the level of pressure relief at the beginning of exhalation is determined by the A-Flex (C-Flex+) setting and the amount of patient flow in any one breath. Note: The patient also has access to this setting, if A-Flex (C-Flex+) is enabled.
Note: A-Flex (C-Flex+) transitions from no A-Flex (C-Flex+) at 4.0 cm H2O to full A-Flex (C-Flex+) at 6 cm H2O. A-Flex (C-Flex+) is top limited at 20.0 cm H2O pressure.
C-Flex+ Pressure Profile
We see few people benefit from C-Flex at higher levels. It is unlike EPR in that C-Flex is predictive and is apparently the main reason the Philips machines commonly miss expiration time. C-Flex does not follow your breathing, it anticipates it and returns IPAP/CPAP pressure well before expiration is completed. This can make it feel like exhaling is cutoff, but in some individuals, it creates hypopnea by not enabling a full exhale (tidal volume). Higher settings seem to amplify this error.