If Germany wins WW1 the British Empire will almost definitely collapse, given that Germany losing WW1 also led to the Empire's collapse. The BE was a very fragile institution that fell apart incredibly quickly once Britain actually had to fight a serious war, and indeed likely would have collapsed even if the Brits didn't fight any big wars.
That said, even if Germany wins it will not be Germany that dismantles the Empire. It will be the same forces that did it OTL, only now strengthened and more confident much earlier. India never had any desire to remain a British cash cow, while the Dominions recognised the limits of Britain's power well before the 20th century and if Britain actually loses a war will become truly independent very quickly, out of necessity not desire. The other colonies were either smaller versions of India that would similar to OTL become independent a little after India did i.e. Malaya etc, or were pretty useless like most of Africa and did not offer much other than secure bases to India.
It's hard to see a scenario in which Germany actually invades the British Isles with a WW1 PoD, and that is what would be necessary to force the British to do anything that major. There is no likely scenario in which Germany can invade Britain in the 1910's, given the massive superiority of the RN, so to do so would involve having a second crack at it for... reasons? Before aircraft became capable of knocking out battleships an 'invasion of Britain' scenario requires Germany to look at the numbers and say "yeah we are cool with losing 50% or more of out battleships in order to beat Britain and effectively handing naval superiority to the Americans". I mean, it's not impossible to make that calculation but there'd need to be really good reasons. I doubt "India would look better in grey" is a persuasive one.
That said, even if Germany wins it will not be Germany that dismantles the Empire. It will be the same forces that did it OTL, only now strengthened and more confident much earlier. India never had any desire to remain a British cash cow, while the Dominions recognised the limits of Britain's power well before the 20th century and if Britain actually loses a war will become truly independent very quickly, out of necessity not desire. The other colonies were either smaller versions of India that would similar to OTL become independent a little after India did i.e. Malaya etc, or were pretty useless like most of Africa and did not offer much other than secure bases to India.
It's hard to see a scenario in which Germany actually invades the British Isles with a WW1 PoD, and that is what would be necessary to force the British to do anything that major. There is no likely scenario in which Germany can invade Britain in the 1910's, given the massive superiority of the RN, so to do so would involve having a second crack at it for... reasons? Before aircraft became capable of knocking out battleships an 'invasion of Britain' scenario requires Germany to look at the numbers and say "yeah we are cool with losing 50% or more of out battleships in order to beat Britain and effectively handing naval superiority to the Americans". I mean, it's not impossible to make that calculation but there'd need to be really good reasons. I doubt "India would look better in grey" is a persuasive one.