Single, multi-, double-sided or spectral coatings...whatever is there or not will not be helped by placing a filter, or several filters, on the front of the lens. Filters today are several orders of magnitude greatly more effective in dealing with flare on either or both sides of the filter; they are often a good choice for hedging the menace on old lenses with known predisposing factors to flare or image degradation from contrasty light sources.
I have never ever experienced noticeable flare in just one of the lenses I have owned for a long time, a Canon TS-E 24mm; probably just one tranny somewhere with a tiny distinct purple-orange spot in the lower right where I captured an 8-point mid-morning sun 20 odd years ago (that would have been with a filter, too).
Flare in a known optic can be very creative as an adjunct to atmosphere. It can be put to excellent creative use in pinhole cameras; by their very design, they can often make it a beautiful feature. But flare — the possibility of it, how much, when and why, does not interest me unless it is something I have to absolutely avoid (based on knowledge of a particular lens) in the composition. All the images in this thread do not trouble me for the presence of flare.
In your last photo sea spray will definitely exacerbate the effect of flare with sun behind it.