"Me voy a ir yendo" Is a very common phrase here at Mexico. As some comments suggest, it doesn't have much sense if you see it from a grammatical point of view. It's mainly used as a way to say goodbye, and it implies that you have to be somewhere else. I recommend you trying to get in a mexican-spanish state of mind if you will, instead of trying to translate everything to english in order to comprehend it. As you may already know, spanish (and mexican spanish) can get weird, so don't give it much thought and try to accept the richness of the language as it is :D

Contrarily to what other posters said, that sentence is correct and not uncommon in colloquial Spanish. Its equivalent in English would be "I'm gonna get going". The construction "voy a ir + another verb in gerund" is used to add a nuance of immediate intention, that you intend to do something or start doing something very soon in the immediate future. Thus, "me voy a ir yendo" means that you are planning to leave right after having uttered that sentence. So that would be it. Hope it's a bit more clear for you now.

"Me voy a ir yendo" doesn't have much sense. You could say "Voy yendo". It depends on that you want to express. Give me an example

NO TIENE SENTIDO ESA ORACIÓN xd