Good news everyone! I think I found out how to paste a URL (or arbitrary text) from your Android clipboard into the Feedly app's "add new content" search field.
Type a character first, then paste next to it.
If you tap and hold on a blank search field, you get a vibration, but no "paste" pop-up. If you tap in the search field, type a letter, then tap again to get a blinking "I bar" cursor, then tap and hold on that cursor, you get a "paste" pop-up.
Or at least, it worked for me running Android 4.2.2 cyanogenmod on an HTC Desire HD "ace", using Feedly 16.1.542; of course, your milage may vary.
