If I delete the game, will I lose my progress?

Provided that you have signed up for an account in Vainglory; your progress is always saved by us safely on our servers.

You can log in and play with your account from any device that is capable running Vainglory. Which actually means that you could even start a game on one device and then swap devices during the middle of the game if needed due to batteries dying or or some other reason.