Is it ok to 'snake' the flow of my schematic?

Do it like this is my advice: -

And keep the symbols the same (i.e. don't flip them).

"Good practice" really means that the schematic should be, first, unambiguous, and then graspable by the largest possible audience. In my experience, that means that you do what @Andyaka suggests.

The only place I wouldn't do that is when there's an obvious feedback loop that has significant circuitry in it -- then there will be a forward path, hopefully with an obvious input on the left and output on the right, and a feedback path from the output side to some summing, multiplying, or other "ing" junction closer to the input side.