Start by using a convert timezone action, then convert UTCnow() from time zone UTC to your local time. Choose Month Day as the output format.
If you want to have only one excel action you can declare a string variable, and then you can dynamically set the table name..
Now that flow knows what day of the month it is, you can setup a switch action. For the "on" clause you'll want to use your converted time output. then in each case put the month day value that you want it to switch to a new table name. Then in the action of the case you put the set variable action and type the name of the table you want to use. Once you have all your case statements defined, switch your table name in the excel action to be the custom value and choose your variable output.