While there is no option to print an image directly from the BeFunky web app, after you've saved your creation, you can print it out from any online or nearby printing services.
When you apply an effect on BeFunky, the result image comes with a DPI value of 96. This is unrelated to image quality, as it's data stored in the image file telling the printer how many dots per inch (DPI) it should print.
For help printing from your desktop computer, please visit the appropriate help page:
To print in the highest DPI possible, you'd need to get a printer that'd allow you to override the value of 96, for 300.
Maximum size you can print:
With a basic BeFunky account, you can save your image to up to 2500px x 2500px and with BeFunky Plus account up to 4000px x 4000px.