B737 MAX 8 Captain reported that after parking at the gate; a ramp agent notified the crew that two main gear tires were smoking and flat. Captain stated were no indications during taxi in of a tire issue.

Narrative

Upon taxiing into Gate XX in ZZZZ operating a 737 Max 8; I set the parking brake. A after the chalks in signal; a few moments later a marshaller pointed to the right side of the aircraft. Confused; I stepped out and company personnel came up and confirmed that both no.3 & no.4 tires were flat with smoke. I went outside and confirmed the same. Landed on Runway XX and it was a smooth touchdown; with brakes 3 set. I disconnected the auto brakes and initiated gradual manual braking in order to exit at Taxiway 1. We exited and had an uneventful slow taxi in with no indication of any jerking nor anything unusual. From my perspective it was a perfectly normal slow taxi in. The brakes seemed to have overheated after we set the parking brake.Called Dispatch; was patched through to Maintenance Control; and explained this exact narrative to them and did an ELB (Electronic Logbook) write up. Informed Operations that FAs (Flight Attendants) stayed on board and for Maintenance Techs to take that into account should they need to perform maintenance.