Personally, I would risk giving these drops to your budgie or any bird. Many of the flowers are safe - I cannot verify that they are all safe. However glycerin is something that should only be given to birds with the utmost care and really isn't necessary for their well being, but can easily make a bird ill or even be lethal.
Given budgies are such small birds, the propensity to overdose the bird with glycerin is even greater.
There is evidence that small amounts of glycerin may assist heat stressed chickens, but the level of glycerin that is beneficial can easily go into a level that has an adverse affect on the birds health. There is a fine line. (1)
From Cornell Lab of Ornithology Bird Note Providing water for birds
Ingesting large amounts of glycerin elevates the blood sugar level of
a bird, which can be harmful or even fatal
Any benefits would be outweighed by the potential side effects.
The better option may be to grow and provide access to the actual flowers for your bird, ensuring that you only use flowers that are safe for your bird.
Here is a list of Bird-Safe Edible Flowers:
African Tulip Tree (Spathodea campanulata)
Apple blossum (Malus domestica)
Bald Cypress (Taxodium distichum)
Basil (Ocimum basilicum)
Bee balm (Monarda)
Borage blossoms (Borago officinalis)
Bottlebrush (Callistemon spp.)
Calendula (Pot Marigold) (Calendula officinalis)
Carnations (Dianthus caryophyllus)
Chamomile (Chamaemelum nobile)
Chives (allium schoenoprasum)
Coriander/cilantro (Coriandrum sativum)
Daises
Dandelion (Taraxacum)
Daylily (Hemerocallis spp.)
Dill (Anethum graveolen)
Elderberry (Sambucus spp.)
Eucalyptus
Fennel (Foeniculum vulgare)
Gardenia (Gardenia jasminoides)
Garlic (Allium sativum L.)
Gladiolus
Grapefruit (Citrus x paradise)
Hibiscus
Honeysuckle (Lonicera)
Impatiens
Jarcaranda (Jacaranda mimosifolia)
Kumquat (various Fortunella species)
Lilac (Oleaceae Syringa)
Lime (Citrus aurantifolia)
Lemon (Citrus × lemon)
Milk thistle (Silybum species)
Melalecuca (Melaleuca quinquinervia)
Nasturtiums
Orchid tree (Bauhinia verigata)
Congrats! You found the spring parrot!
Okra (Abelmoschus esculentus)
Orange (Citrus sinensis)
Oregano (Origanum vulgare)
Pansies (Viola tricolor)
Passion flowers (Passifloraceae Passiflora)
Petunia (Petunia spp.)
Plum (Prunoideae Prunus)
Pumpkin (Cucurbita pepo or Cucurbita mixta)
Roses/Rose hips (Rosoideae Rosa)
Rosemary (Rosmarinus officinalis)
Runner Beans (Phaseolus coccineus)
Sage (Salvia officinalis)
Sunflowers (Helianthus annuus)
Thyme (Lamiaceae Thyme)
Zucchini (Cucurbita pepo.)
Violets (Violaceae Viola)
- Effects of the Addition of Pure Glycerin Supplementation in the Drinking Water on the Performance of Broilers Submitted to Heat Stress and Feed Restriction .
PO MoraesI, et al.
http://dx.doi.org/10.1590/1806-9061-2015-0166