Does a "capacitor" for light exist, which could filter out flickering? If I have a light that is flickering at a frequency low enough to be perceived by the human eye, is there any type of material that exists that will smooth out the appearance of flickering? Similar to how a capacitor smooths the output of a rectifier?
 A: You could argue that this is exactly what glow-in-the-dark materials do.  Phosphorescent materials gather energy in the form of electrons moved to higher potentials. The result is a very lossy low-pass filter on the light received.
The real issue is the lossiness.  Phosphorescent materials are substantially less efficient than a capacitor is.
For further exploration, consider what it means to you to "smooth out the appearance" of flickering, or what it means to "smooth" the output of a rectifier.  The analogy is good for a first pass, but if you really want to get specific regarding what qualifies as a "capacitor for light" and what does not, you may have to dig deeper into properties you wish to see in said capacitor.
A: Yes. You could use a series of Bose Einstein Condensates (BEC), each with a different delay time for light. For example, 1 second up to 10 seconds. Then have a mirror that diverted light arriving at 1 second into the 10 second delay... to light arriving at 10 seconds into the 1 second delay. 
The outputs of the BEC will then offer photons collected over 10 seconds output over 1 second.
A: Phosphor
Phosphor is a material which absorbs light, and then re-emits it a short time later. It is used in some LEDs and CCFL lamps. But:


*

*Most phosphors are colour specific, they absorb a certain colour and re-emit a spread of redder colours. To get a mixture which absorbs and emits mostly-white might not be easy.

*Phosphors have varying time constants, that is some re-emit very quickly, others slower.  You'll have to choose a phosphor which is slow enough to cover the dark time of your flickering lamp.

*I have no idea how you're going to apply a phosphor to an existing light in a way which will last a reasonable time in service and will intercept most of the light. It's going to be hard to do a decent job with paint.


All in all, it will probably be easier to filter the flickering out electronically with a capacitor and/or an inductor.
A: In capacitor we can say that electrons are piling up in one electrode and depleting on the other causing that energy (chage times voltage) is stored there. Hydrodynamical equivalent would be a water tank, where energy is stored proportional to mass times elevation. Photons are "pure energy" - they have no stationary mass and no charge.
Using excitation and deexcitation will be difficult because 


*

*it causes red shift - energy of incident photon must be greter of equal to the energy needed to excitation - so usually you need near UV flickering light to be filtered as smooth visible.

*The available "colours" are limitted by the spectra of the filter.

*The spontaneous radiation is usually fast, so flickering won't be filtered effectively.


All together, it shall be easier to stabilise the light source than to stabilise the light. You can switch back to Edisons light bulb, the cooling of the fillament should be slow enough, or stabilise the power source for continuously glowing source.
A: Such a material would have to absorb light and emit it slowly. A blackbody comes to mind, but this would not be practical if you need to emit visible light. It may be easier to design a circuit which supplies a signal to the light that prevents it from flickering.
A: Some observations that are peripherally on topic, and may be useful:


*

*flickering of light is usually a result of fluctuations in driving voltage (AC)

*effect is more pronounced when light has fast response time (LED, fluorescent bulb); note that white LEDs and fluorescent bulbs both have a phosphor to convert higher energy photons into a spread spectrum

*the emission of the mixed phosphors in white light has different life times:  consequently, if you observe a fluorescent light through a fan, you will actually see a colored fringe - as different colors "decay" at different rates

*Long life time phosphors exist (think luminous dials on a watch), but these have a low intensity: you can only "see" a few atoms deep into the material, and there are a finite number of molecules on the surface. If each of these molecules can emit a single photon upon excitation, then the maximum intensity you can get from the material will be a function of the time constant: longer time, lower intensity.

*All phosphors have losses: high energy in, lower energy out. The difference is heat. This makes "warm" fluorescent lights less efficient (convert UV to red - lose half the energy)

*In applications where flicker free light is needed, several techniques are used:



*

*High frequency converters to create "essentially DC" (using inductors and capacitors to maintain steady current although the input varies; also called switching regulators)

*3 phase drive - 1/3 of lights is driven by each of the three phases, which are 120° out of phase with each other. The net result is that the light output is flicker free to quite a high order (that is, even if the light output is not linear with input voltage).

*High power incandescent light: sufficiently large filaments have such heat capacity that they do not cool noticeably when the current reverses.

*Lead/lag ballast: it is possible, using an LC network, to shift the phase of the current through your load (tip of the hat to @Farcher to bring that up in a comment). This is not quite as effective as the three-phase solution, but it is more readily installed in situations where no three phase supply is available at the point of load. The following diagram (from "Electrical Installation Work: Level 3 EAL Edition" by Peter Roberts) shows what this is, and the effect:




A: Certainly not in the classical sense of a charged plate capacitor.  It is hard enough to find decent capacitor at GHz frequencies, let alone the THz region.
Sorry to answer the question you asked, but I think you are looking for some kind of optical integrator - this could be achieved by signal processing of captured video data or even in real time - but I know of no material that does this.
A: If the flicker is not an "ON/OFF" flicker (not unusual in LEDs, for example) but is more of a ripple, where the brightness dims by 10% or so, then there can be a direct engineering solution: use a photodetector to measure brightness, then feed the signal back to control the drive current to the lamp - or to control the transmissivity of a liquid crystal screen surrounding the lamp.
This can be used to effectively eliminate all ripple whose frequency is less than $1/t$, where $t$ is the delay time in the feedback loop.
