The matrix~ object is a multichannel audio mixer. It’s useful as a mixer of sounds, and also as an audio switcher/router, because you can route any input to any output, with built-in interpolation for smooth, click-free amplitude changes.
The main ways to delay a sound in Max are demonstrated in the examples from this site Simple delay of an audio signal and Delay with tempo-relative timing. You might want to take a look at those examples and read the associated text to review how they work, and what their pros and cons are.
The way we commonly avoid clicks when changing the amplitude of a sound is to interpolate smoothly sample-by-sample from one gain factor to another, using an object such as line~. Does that same technique work well for making a smooth change from one delay time to another? As it turns out, that's not the best way to get a seamless unnoticeable change from one delay time to another, because changing the delay time gradually will actually cause a pitch shift in the sound.
One possible solution to the problem of clicks occurring when delay time is changed is to fade the amplitude of the delayed sound to 0 just before changing the delay time, then fade back up immediately after the change. This does avoid clicks, but causes an audible momentary break or dip in the sound. This shows one way you could implement such momentary "ducking" of the amplitude.
This patch shows several techniques relevant to granular synthesis, playing a stream of short excerpts of recorded sound. (The patch uses one abstraction, called pan~, that's provided in the example titled "Constant-intensity panning subpatch". You'll need to download that abstraction and save it with the name pan~ somewhere in Max's file search path.)
Will need to download the pan~ abstraction found here.
This is a flanger that can easily be used as an abstraction (subpatch) within any audio patch. Simply save this patch in Max's file search path with the file name "flange~.maxpat", and it can then be used as a flange~ object, as shown in the example "Try the flange~ abstraction".
For this example to work properly, you must first download "Abstraction for mixing or crossfading two audio signals" and save it with the name xfade~.maxpat. Then you must ensure that your xfade~.maxpat file is in the Max search path, or you must save this example patch in the same folder as the xfade~.maxpat file and reopen it, so that this patch can find the xfade~ object.
This patch is functionally identical to the mix~ abstraction in "A useful subpatch for mixing and balancing two sounds"; you can read its explanation there. It's repeated here in order to focus on the topic of initialization: setting up the initial state of your program the way you want it.