You will need dependencies on the aseprite page at https://github.com/aseprite/aseprite/blob/main/INSTALL.md#dependencies. Skia is not required, as it is installed by the script.

aseprite-build.sh

#!/bin/bash

OS=$(uname | tr '[:upper:]' '[:lower:]')
ARCH=$(uname -m)

if [[ $OS == "darwin" ]]; then
	if [[ $ARCH == "x86_64" ]]; then
		URL="https://github.com/aseprite/skia/releases/download/m102-861e4743af/Skia-macOS-Release-x64.zip"
	elif [[ $ARCH == "arm64" ]]; then
		URL="https://github.com/aseprite/skia/releases/download/m102-861e4743af/Skia-macOS-Release-arm64.zip"
	fi
elif [[ $OS == "linux" ]]; then
	if [[ $ARCH == "x86_64" ]]; then
		URL="https://github.com/aseprite/skia/releases/download/m102-861e4743af/Skia-Linux-Release-x64-libc++.zip"
	elif [[ $ARCH == "i686" ]]; then
		URL="https://github.com/aseprite/skia/releases/download/m102-861e4743af/Skia-Linux-Release-x86-libc++.zip"
	fi
fi

if [[ $ARCH == "i686" ]]; then
	LIB_ARCH="x86"
elif [[ $ARCH == "x86_64" ]]; then
	LIB_ARCH="x64"
elif [[ $ARCH == "arm64" ]]; then
	LIB_ARCH="arm64"
fi

release_info=$(curl -s "https://api.github.com/repos/aseprite/aseprite/releases/latest")
download_url=$(echo "$release_info" | grep '"browser_download_url":' | sed -E 's/.*"([^"]+)".*/\1/')
wget -O aseprite.zip "$download_url"
wget -O skia.zip $URL

mkdir aseprite
unzip aseprite.zip -d ./aseprite

mkdir skia
unzip skia.zip -d ./skia

cd aseprite
mkdir build
cd build

cmake -G Ninja -DLAF_BACKEND=skia -DSKIA_DIR=../../skia -DSKIA_LIBRARY_DIR=../../skia/out/Release-$LIB_ARCH ..
ninja

cd ../..
mv aseprite/build/bin .
rm -rf aseprite.zip skia.zip aseprite skia

Linux is untested as of now. Linux arm64 is unlikely to be supported in the future due to lack of Skia support.