To record them you need the output of an electrocardiograph and a microphone. The ECG should be sampled at 500 Hz or more and speech at 12 kHz. For synchronising you can add a synchronisation pulse to both signals (simply add signal 1 + pulse as channel 1 and signal 2 + the same pulse as channel 2. This would produce 2 signals with different sampling frequencies. A lazy alternative is to sample both at 12 kHz.
Yes, as Dr. Soares mentioned the real deal is to synchronize both signals. It is typical that you do not have the same sensors, and the same sampling frequency for both signals. So we the most typical way to do it is using the unix time-stamp synchornizing both sensors with the same clock to reduce the lag at maximum. You can do it connecting it to same mobile device or the same computer assuring real-time data collection.