You have one of two possible problems.
1. Toilet is partially clogged. Solution-Auger toilet. Possibly remove from floor and check for obstruction.
2. As you said water not getting from tank to bowl fast enough. Try this first. Pour a bucket of water directly into bowl. If it flushes readily, Your “ports” may be clogged up. You can try to improve this by gently putting a bent paper clip through all the ports on the inside rim of the bowl. Or replace the toilet. Good luck, Jeff