After Feather, the Redeemed got spoiled, it got my brain turning on how replacement effects interact, and I would like to confirm something about cards with Flashback like Sieze the Day or cards that don't normally go to the graveyard after they resolve like Blue Sun's Zenith or Eldritch Evolution. None of those are examples of self-replacement effects, right? I imagine they're not, because they don't replace any written instruction on the spell's effect, but the definition of self-replacement is a bit hazy for me, so I would like to be sure.
An effect that says to put a spell somewhere instead of into its owner's graveyard as it resolves (as found, for example, in Feather's triggered ability, buyback [C.R. 702.26a], and rebound [C.R. 702.87a]) is not a self-replacement effect. An effect that says to exile an object "instead of putting it anywhere else any time it would leave the stack" (as found in flashback [C.R. 702.33a] and aftermath [C.R. 702.126a]) is not a self-replacement effect either. Both kinds of effects interact the same way as most other replacement effects in cases when two or more of them would affect where a spell would go — namely, the controller of that spell chooses which effect applies (C.R. 616.1, 616.1d).
Self-replacement effects are "not continuous effects" (C.R. 614.15). Examples of self-replacement effects are found in Remand, Urza's Mine, Cabal Ritual, and Snowfall (C.R. 108.1). All four of these cards use self-replacement effects to modify how earlier text in the card is to be interpreted (C.R. 614.15; see also C.R. 608.2c). (For Cabal Ritual, the self-replacement effect appears in a separate ability because of the threshold ability word, but it's still considered a spell ability [C.R. 112.3a]). See also this thread.
A self-replacement effect is something like: "Do X. If Y, do Z instead".
For example, "Tap target creature. If NAME was kicked, destroy that creature instead." Or "NAME deals 3 damage to target player. (Line break) Raid - If you attacked with a creature this turn, instead NAME deals 5 damage to that player and the damage can't be prevented."
The second sentence is a self replacement effect that changes what the previous effect of the spell itself does.
The exile part of Flashback is a replacement effect, but it is not changing an effect of the spell itself, so it's not a self-replacement. So you can choose freely between it and Feather's replacement.
Blue Sun's Zenith and Eldritch Evolution don't even have any replacement effects. They are just effects, regular instructions that you follow as they resolve. They are not replacing anything, and happen before the spell would be put on the graveyard by the rules. Feather's replacement effect never gets to apply to them (ignoring the fact they don't target a creature you control anyway).