I will take a stab at your question. First off,I get it that you need to match existing heights.My question,what is this 2.5-3" issue all about ? What is governing that height,existing concrete slab,soil etc.? Reason for asking,IMHO,I feel 2.5"-3" of any mortar is excessive.
The key to any flagging success hinges on several factors. They are base,drainage,substrate,joint size,and ability of stone to bond with the mortar. With that said, a type S mortar with a lime content a bit to the lower side of the scale (yes there is a range for all types) should do the trick both as a setting bed and joints between the stones.
There is a caveat to that though.You can enhance the bond with a slurry or score the backside with an angle grinder. However,the closest thing to a sure fire belt and suspenders approach is to sandblast the backsides with a course aggregate ,a mechanical bush hammer could be used but it is slower and you will break a bunch of stones trying.
After the back is roughed,either apply a portland slurry or a proprietary bonding agent (even to edges of joints) Keep joints to 1/2"or less,do not concave joint but flat join them.Doing so will not leave "troughs" to hold water.