If I got it right, your objective would be to check multiple flags and, depending on their values, send the player to different locations, all in a single transition (via multiple Shifts). This may be impossible, if I remember correctly, because I recall the game has some problems in triggering Flag Warps when the player enters a screen via a Shift.
Let's say you have a switch (a Shift object) that, when activated, sends the player to another screen: in theory, if there's a Flag check in that screen, the player may or may not get warped to an alternative screen depending on the success of said check. This is with a single Flag, yet it might not work for the reason I stated above. However, if it works, you may chain these screens with other Shift/Flag-check screens to create further branches (a series of if-then-else statements).
Other lever makers have used a variation on that, but I'm not sure if it could work for you: basically, they don't use Shifts, but let the player fall through a series of screens with Flag Checks. This always works, but it might not suit everyone's level design. You could make the player fall through screens while covered by a Custom Object foreground, but here we're getting to really complicated stuff.
About World.ini editing, ask me anything: I've never used the Manager because I find it quicker to copy/paste the text file.
; Flag check example
; If Flag 1 is on, move 5 screens to the right
[x1000y1000]
Flag(A)=1
FlagWarpX(A)=5
; Flag toggle example
; Shift A turns Flag 1 on
[x1000y1000]
ShiftFlagOn(A)=1