Job, if this is a program problem, we’ll need more information to try to help, since the play button certainly works on most devices. At least the model and android version of the phone and exact model of any headset you are using. But there are some things you can try yourself…
First, check your recording level…the moving bar across the bottom of the screen. This will confirm that your microphone is picking up something.
When you sync, can you play the recordings on your main computer? If not, the problem may really be the recording process.
If sync confirms that you are getting good recordings, the next thing to check would be volume levels on the phone. Many phones have several volume settings. Try turning them all well up and see if it helps. If so, you can fiddle with them until you work out which one affects HearThis playback.
If you are using a headset, try unplugging it for playback. In fact, experiment with both recording and playback without a headset. I would not recommend this for serious work, but if the program basically works when not using a headset, it’s possible your headset is wired wrongly. Unfortunately there are several common kinds of headset with plugs that will fit the socket on most androids, and some phones need one while others need the other. A headset with a microphone will usually have four connectors (3 plastic bands on the tip separating it into four metal bands, including the tip). But there are at least two ways of connecting this up. See https://help.longtailproducts.com/hc/en-us/articles/207970396-Smartphone-Headset-Standards-Apple-iPhone-AHJ-CTIA-OMTP.
If you are using a Bluetooth headset, inability to play back is a known problem, for which I haven’t been able to find a fix. Maybe I will eventually. For some reason, it seems to be really hard to get an Android to use a bluetooth headset for anything but phone calls. Try a regular (or usb) headset.