First off, I am very happy to see you are starting by saving your own money. The ability to manage your own finances is foundational to any investment plan and far too many skip that step.
Have you read, "Investing In Real Estate With No (And Low) Money Down" by @Brandon Turner ? I disagree with the basic premise of "easy" money but the book has a lot of good ideas on how you can fund investments through creative financing.
One of my favorites is owner financing where you essentially make payments to the owner instead of a bank. The owner typically won't run a credit check or care about your income:debt ratio which makes this a great option. I recently bought six units by putting down 10% and then setting up payments with the owner at 5% interest. We agreed on a "balloon" payment in five years which means I will need to obtain a traditional bank loan at that point so I can pay the owner his remaining lump sum. Qualifying with a bank will be easy at that point because the property value should appraise far above the purchase price and I'll have five years of income history to prove it's a solid investment.
Anyway, I recommend Brandon's book because it gives an overview of so many different ways to obtain financing. Pick one, study it, and then give it a shot.
And, side note, "The Book on Flipping Houses" and "The Book on Estimating Rehab Costs" by @J Scott are currently in the revision process, which sound right up your alley! The first editions are available now, and the new editions will be out in January.
Hope this helps! Good luck on your flipping endeavors.