Q.How Do I Get My Honeysuckle to Grow Faster and Produce Blooms
I have 4 plants. 3 are growing okay, but only one gets flowers. The 4th one is alive, but doesn’t seem to be progressing at all. All were planted around a pergola under the same conditions.

Certified GKH Gardening Expert
while the conditions may seem all the same, they can vary for locations even just a few feet apart. I would recommend that you give them all a phosphorous heavy fertilizer. This will help with blooming. Check also the light conditions and how well water is penetrating the soil at the base of each plant.
Pests may also be affecting the plants to different degrees. Check the plants carefully for pests or you can simply treat the plants with a pesticide as a precaution.