The best open source alternative to BeFunky is PixelFed, which is both free and Open Source. If that doesn't suit you, our users have ranked more than 25 alternatives to BeFunky and three of them is open source so hopefully you can find a suitable replacement. Other interesting open source alternatives to BeFunky are BitMappery (Free, Open Source) and Free Online Photoshop (Free, Open Source).
Pixelfed is an image sharing platform with focus on Privacy, Safety and Security, an ethical alternative to centralized platforms like Instagram. Federated, Ad-Free, No algorithms, No 3rd party analytics or tracking. Can run on your own server.
Photoshop in the browser? Photoshop ? Flattering, but not quite. BitMappery does however allow you to import photos, apply transformations, tweak filters and draw masks in a non-destructive manner. It has some overlap in functionality but is definitely a more simple product.