Sorry if this is a frequent noob and/or stupid question, but how does order flow relate to auction market theory and/or volume spread analysis?
The short answer is, they are not at all related. From what I can tell of AMT, it is an extrapolation of price history data to show where price has spent the majority of its time. In theory, if you know where price has spent the most time, you can infer where "True value" resides. With this info in hand, you can arb out any deviation from that value.
Vsa tries to do the same thing but under a slightly different premise. Instead of calling the price at which a majority of the volume traded true value, VSA assumes that there is some big player(s) acting at those levels to manipulate price. Supposebly once you find evidence of this manipulation, you can then infer a directional bias of the market and trade accordingly.
What both of these systems(strategies?) have in common is that they extract all their information from the chart. Presumably, external factors will manifest themselves in price data, so it isn't important to consider those external factors in your trading decisions.
In short, order flow trading is a metagame analysis system for predicting the future course of price change. By focusing ones effort on making quality predictions, high probability trades can be entered in the present. To accomplish that goal, Order Flow Traders focus the majority of their analysis on external factors like participant strategy, fundamental factors (news/data/etc), and microstructure processes.
Order Flow Trading is catagorically at odds with both ATM and VSA because they start from vastly dffierent assumptions about the path to profits. While VSA and ATM follow some amalgamtion of the efficient market hypothesis and behavior finance theory, OF rejects both as fatally flawed concepts. Further, while VSA and ATM seek to distill historic price data into an indicator based method of point and click, OF focuses on learning how to analyze external information for discretionary trade execution.
Now I'm not saying that VSA or ATM are bad strategies or that you can't make money with them (I have absolutly no idea with regard to their merits and don't really care to find out), I'm only pointing out that they are not at all related to order flow trading.
Hope that helps. Luck be with you.