Many smart grid communications are delay sensitive and have very strict timing requirements for message deliveries. For example, trip protection messages must be delivered to the destination within 3 ms according to IEC 61850. Such time-critical communications are vulnerable to flooding attacks which attempt to increase message delivery delay through congesting the network channel and exhausting the computation resources of the communicating nodes. However, there is a lack of understanding on how much flooding attacks affect message delivery delays. In this paper, we conduct experimental studies to investigate how flooding attacks affect message delivery delays for time-critical communications in smart grid. Our experiments are based on both wireless networks in a lab and wired networks in a real, industry-standard electric power facility. Experimental results show that even low-rate flooding attacks can significantly increase the message delivery delays, especially when wireless networks are used.