Meaning of "build-up"

The phrase 'build-up' generally means the gentle accumulation or slow increase of something (for example, of plaque on unbrushed teeth). Occasionally, it is not so slow (as in a build-up of troops before an invasion). In this context, it really means something like 'which can cause a build-up of residual chemicals on the hair, ...'.

Build-up in this instance means that residue of the hair product is left behind and accumulates, causing the mentioned effects.

"Hair Build-up" is a layer of chemicals that haven't been washed away, usually caused by shampoos, or hair stylers like gel.

From a hair-care site:

Buildup occurs when:

Certain products like non-water soluble waxes are used to style the hair.
2 in 1 shampoos are used continuously.
Certain shampoos cause buildup due to the type of cheaper ingredients they use to give instant combability. These can form a film on the hair or you may have to use a large amount to make your hair feel clean also resulting in buildup.
Hair sprays applied too close and in too strong a concentration to one area e.g. the fringe, leave a flaking powder on the hair after brushing.
If gel is applied in a blob it cannot spread through the rest of the hair causing build-up on that spot. We sometimes find that wetting your hands before getting the gel out of the pot and mixing it can solve this problem.