Hi, I moved funds from a Simple IRA and a 401k into a Traditional IRA this year. Do I report the combined amount (or either of these amounts) as "the total amount I put into a Traditional IRA"?

If you are in the Deductions and Credits section of your return working on Traditional IRA contributions, then the answer is no, you do not enter either amount. 

Transferring or moving funds from one type of account to another (Traditional IRA) does not count as a contribution to the IRA.  Instead, this type of transaction is considered a rollover. 

You should have received a Form 1099-R for each of the distributions (from the SIMPLE IRA and the 401k).  You would enter this information into your tax return and answer the follow-up questions about what you did with the money.  The answers to these questions will show that the money went into a Traditional IRA.  You do not need to make another entry in the Deductions and Credits section of your return to report it.