My lime tree cutting is about 2 months along and it has not produced any new leaves but is producing flower buds along the stem. Should I be seeing new leave growth?
It sounds like the cutting has come from the wrong part of the tree and may not work as a cutting to develop a new plant. When a fruit tree grows it produces two types of wood, vegetative and flower/fruit producing. Distinguishing signs vary, but for many trees the vegetative buds are long and pointy and the flowering buds are squat, fat and blunt. Once cut, a flowering shoot will undergo stress which forces it to expand buds as you can see in your case.
For propagation we use the first type, vegetative cuttings that have not developed fruit producing buds. Your cutting may produce a few leaves but won't really have the internal chemistry to go on to readily produce roots.
If this is the only cutting you can obtain and you wish to try to make it root, remove the flowers and leave it to produce as many leaves as it can. If any nodes produce only leaves and no flowers you may be in with a chance. Otherwise if no leaves appear the chance of roots forming is low.
To force the tree to produce vegetative shoots for making cuttings you can cut back a vigorous branch; this will result in the branch producing new vegetative shoots which can be used for rooting or grafting.