Not sure what the fixation with Trump's taxes are. They wouldn't show any "Russian connections" (or anything of that sort) since that information isn't required to be disclosed.You've got it backwards. He was lying about being wiretapped by Obama for political purposes, who doesn't have the power to direct law enforcement surveillance of citizens. (No President does.) If there was surveillance of someone on Trump's organization (Flynn, Manafort) it would be because the Justice Dept. and FBI directed it through a FISA court. Trump's lying about it to muddy the water about his many Russian connections. (And more we likely don't know about because he refuses to release his taxes.)
Anyway, the leaks in the early days were almost certainly from Obama-era holdovers, and politically motivated.
Regarding the Flynn leaks, it could well be that the DOJ has a wiretap order on the Russian ambassador, which means that they have records of conversations with leaders on both sides of the political aisle. I'm sure someone so politically motivated could find something damaging a Democrat said to the ambassador.