Reproduced you issue, have the same error.

minikube v1.7.2 on Centos 7.7.1908
Docker 19.03.5
vm-driver=virtualbox

Connecting cluster to "Old Tree 34" (id: old-tree-34) on Weave Cloud
Installing Weave Cloud agents on minikube at https://192.168.99.100:8443
Performing a check of the Kubernetes installation setup.
There was an error while performing a DNS check: checking DNS failed, the DNS in the Kubernetes cluster is not working correctly. Please check that your cluster can download images and run pods.

I wasnt able to fix this problem, instead of that found a workaround - use Helm. You have second tab 'Helm 'in 'Install the Weave Cloud Agents' with provided command, like

helm repo update && helm upgrade --install --wait weave-cloud \
  --set token=xxx \
  --namespace weave \
  stable/weave-cloud

Lets install Helm and use it.

curl https://raw.githubusercontent.com/helm/helm/master/scripts/get | bash
kubectl create serviceaccount --namespace kube-system tiller
kubectl create clusterrolebinding tiller-cluster-rule --clusterrole=cluster-admin --serviceaccount=kube-system:tiller
helm init --service-account tiller
.....
Tiller (the Helm server-side component) has been installed into your Kubernetes Cluster.


helm repo update
helm upgrade --install --wait weave-cloud \
>   --set token=xxx \
>   --namespace weave \
>   stable/weave-cloud



Release "weave-cloud" does not exist. Installing it now.    

NAME:   weave-cloud
LAST DEPLOYED: Thu Feb 13 14:52:45 2020
NAMESPACE: weave
STATUS: DEPLOYED

RESOURCES:
==> v1/Deployment
NAME         AGE
weave-agent  35s

==> v1/Pod(related)
NAME                          AGE
weave-agent-69fbf74889-dw77c  35s

==> v1/Secret
NAME         AGE
weave-cloud  35s

==> v1/ServiceAccount
NAME         AGE
weave-cloud  35s

==> v1beta1/ClusterRole
NAME         AGE
weave-cloud  35s

==> v1beta1/ClusterRoleBinding
NAME         AGE
weave-cloud  35s


NOTES:
Weave Cloud agents had been installed!

First, verify all Pods are running:

  kubectl get pods -n weave

Next, login to Weave Cloud (https://cloud.weave.works) and verify the agents are connect to your instance.

If you need help or have any question, join our Slack to chat to us – https://slack.weave.works.

Happy hacking!

Check(wait around 10 min to deploy everything):

kubectl get pods -n weave
NAME                                        READY   STATUS    RESTARTS   AGE
kube-state-metrics-64599b7996-d8pnw         1/1     Running   0          29m
prom-node-exporter-2lwbn                    1/1     Running   0          29m
prometheus-5586cdd667-dtdqq                 2/2     Running   0          29m
weave-agent-6c77dbc569-xc9qx                1/1     Running   0          29m
weave-flux-agent-65cb4694d8-sllks           1/1     Running   0          29m
weave-flux-memcached-676f88fcf7-ktwnp       1/1     Running   0          29m
weave-scope-agent-7lgll                     1/1     Running   0          29m
weave-scope-cluster-agent-8fb596b6b-mddv8   1/1     Running   0          29m
[vkryvoruchko@nested-vm-image1 bin]$ kubectl get all -n weave
NAME                                            READY   STATUS    RESTARTS   AGE
pod/kube-state-metrics-64599b7996-d8pnw         1/1     Running   0          30m
pod/prom-node-exporter-2lwbn                    1/1     Running   0          30m
pod/prometheus-5586cdd667-dtdqq                 2/2     Running   0          30m
pod/weave-agent-6c77dbc569-xc9qx                1/1     Running   0          30m
pod/weave-flux-agent-65cb4694d8-sllks           1/1     Running   0          30m
pod/weave-flux-memcached-676f88fcf7-ktwnp       1/1     Running   0          30m
pod/weave-scope-agent-7lgll                     1/1     Running   0          30m
pod/weave-scope-cluster-agent-8fb596b6b-mddv8   1/1     Running   0          30m

NAME                           TYPE        CLUSTER-IP      EXTERNAL-IP   PORT(S)     AGE
service/prometheus             ClusterIP   10.108.197.29   <none>        80/TCP      30m
service/weave-flux-memcached   ClusterIP   None            <none>        11211/TCP   30m

NAME                                DESIRED   CURRENT   READY   UP-TO-DATE   AVAILABLE   NODE SELECTOR   AGE
daemonset.apps/prom-node-exporter   1         1         1       1            1           <none>          30m
daemonset.apps/weave-scope-agent    1         1         1       1            1           <none>          30m

NAME                                        READY   UP-TO-DATE   AVAILABLE   AGE
deployment.apps/kube-state-metrics          1/1     1            1           30m
deployment.apps/prometheus                  1/1     1            1           30m
deployment.apps/weave-agent                 1/1     1            1           31m
deployment.apps/weave-flux-agent            1/1     1            1           30m
deployment.apps/weave-flux-memcached        1/1     1            1           30m
deployment.apps/weave-scope-cluster-agent   1/1     1            1           30m

NAME                                                  DESIRED   CURRENT   READY   AGE
replicaset.apps/kube-state-metrics-64599b7996         1         1         1       30m
replicaset.apps/prometheus-5586cdd667                 1         1         1       30m
replicaset.apps/weave-agent-69fbf74889                0         0         0       31m
replicaset.apps/weave-agent-6c77dbc569                1         1         1       30m
replicaset.apps/weave-flux-agent-65cb4694d8           1         1         1       30m
replicaset.apps/weave-flux-memcached-676f88fcf7       1         1         1       30m
replicaset.apps/weave-scope-cluster-agent-8fb596b6b   1         1         1       30m

Login to https://cloud.weave.works/ and check the same:

Started installing agents on Kubernetes cluster v1.17.2
All Weave Cloud agents are connected!