The city of Kraków has declared an emergency flood (powodzi) alert, and convened the city’s crisis management team in response to widespread flooding, which has brought severe disruption to traffic and transportation.
UPDATE 2134 Thu 23/5/19:
According to the latest data, the culminating wave on the Vistula will go earlier than forecast – on Friday before noon, not on Saturday and will be lower. The water level should not exceed 5.7-5.8 meters. Earlier, it was talked about 7 meters. pic.twitter.com/LQzn8jlZJy
– Radio Krakow (@RadioKrakow) May 23, 2019
UPDATE
A timelapse film of the rising water level on the Wisła basin over the past 24 hrs.
Film by Pawel Jarzębińskiemu
The city has prepared large quantities of sand bags and are installing the flood barriers, closing the gaps in the walls along the Wisła boulevards.
According to the forecasts of the Institute of Meteorology and Water Management, on Saturday, 25th May, the Wisła water level (measured on a water gauge in Bielany) could reach 7m (the alarm level is 5.2 meters). More details here. 
The following resources will help you keep up to date with the current situation:
KRAKÓW LIVE: flood situation in the city (official city live updates)
Live Webcam – Wawel/Wisła basin
Utrudnienia na Krakowskich drogach (FB Group showing road difficulties)
Platforma Komunikacyjna Krakowa – PKK (Tram disruption updates)
PKK are using the hashtag #utrudnienia_pkk
Policja Małopolska – Kraków Twitter
https://twitter.com/krakow_pl
The floods are reminiscent of severe flooding in Kraków, and across Poland, in May 2010
May 2010 Kraków Flood – Photos
Read our article on the 2010 flood.