So with 52.19 units profit over 707 plays, your edge is 7.38% per bet. Now, your P-value is about 2.5%, which means that the odds your results are due to chance are 1 in 40. So we're not all that certain that you can maintain that 7.38% edge over the long term. If I were you I would round down to 5%.
In short, it means that at full Kelly, if you were to place only one coin-flip bet at a time, you would bet 5% of your bankroll on every play. With two coin-flip bets on separate events, you would bet 4.75% on each as per the calculator. That is, indeed, extremely aggressive.
I would do half-Kelly if I were you, but it all depends on your risk tolerance, how much money you're starting with and all that.