So considering I have the following example:
CompletionStage<String> tokenFuture = getToken();
CompletionStage<CompletionStage<CompletionStage<CompletionStage<Boolean>>>> result = tokenFuture.thenApply(token -> {
    WSRequest request = ws.url(url).setHeader("Authorization", "Bearer " + token);
    CompletionStage<WSResponse> response = request.post(json);
    return response.thenApply(r -> {
        if (r.getStatus() == 201) {
            return CompletableFuture.supplyAsync(() -> CompletableFuture.supplyAsync(() -> true));
        } else {
            return getToken().thenApply(t -> {
                WSRequest req = ws.url(url).setHeader("Authorization", "Bearer " + t);
                return req.post(json).thenApply(b -> b.getStatus() == 201);
            });
        }
    });
});
My problem is with the whole CompletionStage<CompletionStage<CompletionStage<CompletionStage<Boolean>>>> multi nested future type. Is it possible to reduce it to just CompletionStage<Boolean> by using something like flatMap in Scala or is there another way to do this?
Yes, you are looking for the thenCompose(fn) operation:
Returns a new CompletionStage that, when this stage completes normally, is executed with this stage as the argument to the supplied function.
This method takes a function as parameter that takes the result of this completion stage and returns another completion stage.
As such, you could have the following:
CompletionStage<String> tokenFuture = getToken();
CompletionStage<Boolean> result = tokenFuture.thenCompose(token -> {
    WSRequest request = ws.url(url).setHeader("Authorization", "Bearer " + token);
    CompletionStage<WSResponse> response = request.post(json);
    return response.thenCompose(r -> {
        if (r.getStatus() == 201) {
            return CompletableFuture.supplyAsync(() -> true);
        } else {
            return getToken().thenCompose(t -> {
                WSRequest req = ws.url(url).setHeader("Authorization", "Bearer " + t);
                return req.post(json).thenApply(b -> b.getStatus() == 201);
            });
        }
    });
});
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