The frame should have horizontal slots that the wheel axle fits into, and is secured with large nuts on the threaded axle ends. Chain tension is adjusted by moving the whole wheel within these slots.

Park Tool has a video on single speed chain installation and adjustment that you may find helpful to adjust the chain tension correctly.

As noted in comments, you should check that the chain is not worn out. (The pins and bushings wear and become slightly looser which causes the chain to elongate). A worn chain accelerates wear on the sprockets.

There are two mechanisms for chain adjustment on non-derailleur bikes, either: the frame should have horizontal slots that the wheel axle fits into, and is secured with large nuts on the threaded axle ends. Chain tension is adjusted by moving the whole wheel within these slots; or the bottom bracket is mounted in a eccentric cylinder in a oversize bottom bracket shell.

Park Tool has a video on single speed chain installation and adjustment that you may find helpful to adjust the chain tension correctly.

As noted in comments, you should check that the chain is not worn out. (The pins and bushings wear and become slightly looser which causes the chain to elongate). A worn chain accelerates wear on the sprockets.