How to Create a Simple Speaker Driver After LMC555 with Low Pass Filter
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Green box: addition of a DC-blocking (decoupling) capacitor to the output to drive the speaker safely. Orange box: addition of line-level output to drive an audio amplifier.

First, lets fix the existing circuit. Loudspeakers don't like DC. It biases the operation to one side of the suspension's neutral point. They prefer AC. Addition of a decoupling capacitor will fix the DC part. You'll have to experiment with R5 but anything up to 20 Ω should work. That should get you a reasonable tone.

To connect to an amplifier add the components in the orange box. This will reduce the output voltage by a factor of about 10. Adjust the resistors if you want more. By adding capacitance in parallel with R7 you can attenuate high frequencies (which has the effect of rounding off the corners of the square-waves).