Could a creature which lays amniote-like eggs evolve into a creature similar to modern amphibians? The creature would be amphibious, spending most of their time in freshwater, and coming onto land to lay eggs, which would hatch into terrestrial larvae, which, rather than eating a unique diet like real modern amphibians, would be mostly lecithotrophic, with their diet supplemented by their adult diet. The adults would have simpler organs, and moist skin to extract oxygen from water, like modern amphibians. However, they would have flippers instead of legs, as these creatures would be more aquatic
There are much easier ways to go about doing what you want. For one, moist skin allowing oxygen to be extracted from the water is a synapomorphy of Lissamphibia, not amphibians as a whole. Most extinct "amphibians" (temnospondyls, anthracosaurs, semouriamorphs, lepospondyls, stem stegocephalians, colosteids) had either keratinous scales or some form of warty or thickened skin that allowed them to spend a considerable amount of time out of the water (groups like colosteids and stegocephalians didn't, but that's more because they didn't have legs that worked on land). However, all of these species that could breathe water had either external gills like a mudpuppy, or internal gill arches inherited from a fish-like ancestor (e.g., stegocephalians like Acanthostega, colosteids like Greerepeton).
Perhaps most notable for your purposes are the semouriamorphs, which are known to have a terrestrial adult phase that appeared to have had some form of thickened skin but have aquatic forms with external gills (e.g., Discosauriscus). This is still "aquatic larva, terrestrial adult", but at least it's possible to have reptile-like and amphibian-like stages of one's lifecycle.
Notably, true gills have never been re-evolved in Amniota after being lost. No clue if that's because they can't be, because the gill arches are still present embryonically, or if they can't because they run into competition with lissamphibians. However, several species of reptiles have the ability to absorb oxygen from the surrounding water. Sea snakes can absorb oxygen directly through their skin that accounts for 25% of all their oxygen needs, and many turtles are able to respire through their cloaca when underwater hibernating in soil. These reptiles notably do this without losing their scaly skin, and in ways that make them less vulnerable to the downsides of having a cutaneous, mucous-coated skin (e.g., susceptibility to toxins).
More broadly, there are severe ecological consequences to having a terrestrial offspring but aquatic adults.
- Having near-obligately aquatic adults means that your adults cannot easily leave the bodies of water they live in if there is a drought, a red tide/eutrophication, or other disasters that make the body of water uninhabitable.
- Additionally, your reproductive-age adults cannot easily disperse to new populations, making them very vulnerable to reproductive isolation and inbreeding. A good example of this is how global lissamphibian diversity has been gradually shaved away over time (e.g., there used to be salamanders on every continental landmass (based on fossils), but today salamanders are absent from Africa, western Asia, most of South America, and all of Oceania), and most of those belong to a single family (Salamandridae, coincidentally the least water-dependent) due to being very environmentally isolated.
- The juveniles are able to disperse, but smaller organisms have a harder time dispersing to new environments because they have less fat reserves and the distance between habitats represents a longer distance relative to body length (big animals migrate easier).
- Having cutaneous skin comes with some big side effects. Notably an increased vulnerability to environmental toxins (there's a reason chytrid fungus kills frogs and not lizards), and the fact that at larger sizes your species would struggle to obtain enough oxygen due to the square-cubed law. This is why the giant salamanders Andrias and Cryptobranchus are so wrinkly looking and live such low-activity lifestyles. Having complex, highly-enfolded organs like gills or a complex rectum would work better.
- A better idea would be to have the adults retain the ability to stay on land for prolonged periods anyway. There's generally a reason why many littoral niches throughout history have been increasingly occupied by amniotes (e.g., crocodiles, aquatic lizards, turtles, aquatic snakes) instead of amphibians. A broader question would be this: what can your species do that an appropriately-sized crocodilian cannot accomplish already?
It's turtles all the way down the list.
- Most of the time in freshwater: check. Bog turtle, say.
- Brief period on land for larvae that return to the water to feed: check.
- Flattened limbs: check.
- Moist skin to absorb oxygen: check! seriously! The caveat is that it's only during hibernation - their needs are too much when they're active. For now. Evolution hasn't stopped doing its thing!