I think your problem is in the pwd part of the export command.
Replace the single quotes in 'pwd' with Backtick/back quote (``) like this
export PATH="$PATH:`pwd`/flutter/bin"
EDITED
Above command will just work until you close the terminal.
To make the change permanent you have to edit the .bashrc (or .zshrc, etc), using a text editor like vim, gedit or nano and place the same command at the end of the file.
vim ~/.bashrc or nano ~/.bashrc
Add the next line at the end of the file
# Add flutter to the path
export PATH="$PATH:`pwd`/flutter/bin"
Restart your terminal and verify that your PATH was set correctly with the echo $PATH command
Good luck!!