The original question was about what effect flaps had
on aileron efficiency. I presumed this to mean a wing
with no interconnection between flaps and ailerons
and definitely not a wing with flaperons.

I've flown a 15-meter glider with no *rolling* connection between flaps and
ailerons since 1981. By 'no rolling connection' I mean only ailerons impart
roll, regardless of flap position...the flaps lack capability for
differential movement. On this particular ship, assuming neutral
roll-stick, at zero and negative flap settings the entire trailing edge is
in-line (i.e. ailerons and flaps camber-track identically). During the
camber-changing portion of positive flap deflection, the flaps droop twice
as much as the ailerons. Once the ailerons have reached 'max droop' they
remain there while the flaps continue down to ~75-degrees for glide path
control.

From the pilot's perspective, when the ship is on the ground, at
low/early-in-takeoff-roll/post-landing-rollout speeds, the ailerons are
distinctly most effective with flaps negative, less so with flaps neutral
and worst with flaps positive. (Experimenting - ahem, 'roll playing!' -
with a stationary glider, whether flapped and/or spoilered, etc., in a
steady headwind is recommended for the curious. If 'it' happens - i.e.
altered aileron effectiveness - it must be possible.)

For the purposes of the following discussion, I'll take the paraphrased
question about 'what effect flaps had on aileron efficiency' to mean 'what
effect flap position has on perceived aileron effectiveness at
low-relative-wind speeds.'

Though there may be an exception or two out there (I know of none), in
general, negative flaps early in the roll make ailerons 'more effective.'
One way to view why this is so is inertially. In a given state (i.e.
un/partially/fully ballasted), any glider has its minimum roll inertia at
zero airspeed. Any lift created by air flowing past the wing effectively
increases roll inertia by 'stiffening' the glider in roll, meaning aileron
effect will be diminished from what it would be if (say) the air flowed ONLY
over the wings over the span of the ailerons. In other words, anything that
can be done to minimize lift produced from the aileron-less portion of the
wings is to the relative good of maximizing the ailerons' roll
effectiveness. I suspect this relative reduction in roll inertia is the
largest contributor to the 'improved aileron effect.' (Consider fully
ballasted roll inertial effects for example...assuming an equal and
nominally good wing run, which is more likely to drop a wing, a ballasted or
an unballasted otherwise identical glider? For skeptics who claim I'm
confusing aerodynamic effects with mass/inertial effects, F=ma.)

With such
a wing in mind, it appears to me that any effect the
flap setting would have on the aileron would be the
disturbance the flap causes at its outboard end and
across the inboard end of the aileron. I'd like to
read something about that. (I'm no aerodynamicist,
and have no mathematical skill.)

Any break in the trailing edge between flap and aileron will indeed have
some 2nd-order (e.g. transverse airflow) aerodynamic effects beyond the
1st-order (i.e. 2-dimensional-flow-based) ones...exactly zero of which will
be distinguishable to the pilot in the cockpit. Additionally, Todd
Pattist's conception of what's happening when viewing things from the
perspective of the lift-curve vs. angle-of-attack is on-target...but again,
the extent a pilot in the cockpit actually *uses* these sorts of thoughts in
the heat of the moment is debatable. Prioritizing things, it seems to me
what matters to a (non ab-initio) PIC's perspective is: 1) s/he conceptually
grasps 'what's likely to happen when,' maximizing chances of remaining ahead
of the plane and doing the right things in a timely manner, prior to 2)
comprehending 'technically why'. If one's grasp of 'technically why' is
missing, incomplete or downright inaccurate at mathematical or scientific
levels, it matters not so long as it doesn't interfere with 'conceptual
reality,' in which case "No harm, no foul," applies.

For me, having some grasp of 'technically why' helps me remember 'conceptual
reality.' Ideally that grasp will also be accurate, of course!

Regards,
Bob W.