Thanks for the hint.
As I'm not that experienced with the model definitions I had to look some up, but I got it to work.
I now use the following model (if someone has the same problem)
{
"parent": "block/block",
"textures": {
"all": "icedresources:blocks/base_block"
},
"elements": [
{
"from": [ 0, 0, 0 ],
"to": [ 16, 16, 16 ],
"faces": {
"north": { "uv": [ 0, 0, 16, 16 ], "texture": "#all", "tintindex": 0 },
"east": { "uv": [ 0, 0, 16, 16 ], "texture": "#all", "tintindex": 0 },
"south": { "uv": [ 0, 0, 16, 16 ], "texture": "#all", "tintindex": 0 },
"west": { "uv": [ 0, 0, 16, 16 ], "texture": "#all", "tintindex": 0 },
"up": { "uv": [ 0, 0, 16, 16 ], "texture": "#all", "tintindex": 0 },
"down": { "uv": [ 0, 0, 16, 16 ], "texture": "#all", "tintindex": 0 }
}
}
]
}
Just change the block Texture and you can use it as a template/parent in your flat blocks you want to tint.
And your specific block.json files can then be as slim as:
{
"parent": "icedresources:block/base_block"
}