As the other answer states, the source of the initial claim can be traced back as follows:
- Trump's Twitter, quoting
- OANN report, quoting
- anonymous blog post at "Conservative Treehouse", quoting
- anonymous YouTube video "Martin Gugino Attempting A Drive-By-NFC-Hack To Obtain Personal Information From The Buffalo Police" and anonymous Twitter thread
The video shows Martin Gugino holding his phone below eyeline and facing it towards the faces of the police.
The Twitter thread is incoherent. It describes how an IMSI (International Mobile Subscriber Identity) number might be captured by standing outside a home and given to the police to help them obtain a warrant. This has nothing to do with waving a phone at police. According to the EFF, cell phone signals can only be tracked by cell towers, or by a "technically sophisticated organization" capable of simulating a cell tower, which would certainly require a lot of electricity at the very least. A political activist cannot accomplish anything with an IMSI.
The video claims something even stranger, that he is capturing the phone's NFC (near-field communication) signal. This is a chip inside modern credit cards and cell phones used for touch-to-pay. The police have not claimed that this man was reading NFC data, and the phone would have to be much closer to obtain such data. Even if such data was captured through a hitherto unknown NFC spy app, it would be the equivalent of the police officer's credit card, not any secret police information.
The Occam's Razor explanation is that Martin Gugino was pointing his phone at the police because he was filming them; furthermore that the police knocked him over and that he was admitted to the hospital in critical condition, where he remains as of June 10, 2020.