Checking accounts do not affect your credit (FICO score) unless you get a negative balance and the bank closes the account. They DO show up on your ChexSystems which may or may not be an issue. Some banks are more sensitive than others but GENERALLY the issue you might have by opening too many accounts in a short period of time would be being declined for a new account in the future.
I can say it's not likely to ever be a problem. I've opened about 5 accounts in the past 9 months for bonuses and JUST (as in 10 minutes ago) opened another at a bank that is VERY ChexSystems sensitive and had no problems opening the account.
There are reasons that a body stays in motion
At the moment only demons come to mind