No seriously it wasn't an issue for me (is it really one for you?).
I just hit the smiley icon above my Android phones keyboard (at the top left) then I selected whichever emojis that I wanted to use the same as typing any other letter.
See pic of my keyboard in my next comment (since I have no idea what type of phone that you have) or if you're on a laptop or some other device?.
Other than that the only other emoji that I've used on imgflip is the cat 🐱 which I just copypasta in to my notepad app (any app that can handle emojis will do) then I copypasta it from notepad each time that I want to set him free again.
So if it really is an issue for you just copy & paste them in that way!.. Slow but it works.. at least it does for me.
I'll see if I can find an emoji site link that I think I saved into a note file & I will paste it in a comment in a while incase you have no emoji's to hand, just go to the website, select all of the emojis, then copy & paste them into a notepad app for later use.