I have done three annual cash flow statements broken down by month. Do I carry the ending cash balance forward from year one to year two's beginning cash balance?

If I do it throws my 2nd year Balance sheet off by an equal amount.

I don't understand why this would be throwing off your balance sheet. Whatever you have in cash at the end of one year will be the beginning balance for the next year. There's isn't any choice about it. If you ended Dec. 31 with $150 in your checking account, the morning of Jan. 1 when you get up, it simple will still be $150. If something has happened to it, then you have a transaction to be recorded and it's no longer a beginning balance.

This also is not really relevant to the cash flow. Your cash flows should be done off the balance sheet (and other information) anyway. The cash flow should have the change in cash, added to the beginning balance from that year, which gives you the ending balancing for that same year. That same ending balance is the one on your balance sheet. And that balance is carried forward.

When you do the cash flow for the next year, you again get your net cash flow, add the beginning balance (ending balance from last yer), add it, etc.

Something has to be wrong somewhere else, because all ending balances from one year (for permanent accounts) become beginning balances for the next year. The only exception that could possibly exist is if there had been an error somewhere that needed corrected, and even then, something was in error so it kind of doesn't count.