You shouldn’t really have to worry about copyright on Imgflip at all. Any image templates you use are most likely going to be established templates (Bad Luck Brian, Woman Yelling at Cat, etc...), public figures (celebrities, politicians, Youtubers,...) or your personal content (photos, videos, artwork you created). Established templates and public figures fall under fair use, so anyone is free to use them to make memes as long as you’re not monetizing them, I believe. Obviously you don’t have to ask yourself for permission to use your own content. If you were to use content that doesn’t fall under any of these categories however, I would still say you’re in the clear. Worst case scenario, the copyright owner would get in contact with us and we would just remove the specified content. I don’t recall that ever happening though as long as I have been on the site.
Hopefully this helps you get a better idea of what to be aware of. Feel free to ask any questions if you’re still unsure and I’ll do what I can to make sure you get the best answer possible.